PE5MA 5-7
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Questions and Answers

What practical skill does understanding division primarily aid in, according to the text?

  • Understanding historical timelines.
  • Predicting weather patterns.
  • Budgeting and resource allocation. (correct)
  • Calculating the area of geometric shapes.

If you have 350 books and want to arrange them into groups of 25, what mathematical operation will help determine the number of groups?

  • Subtraction
  • Addition
  • Multiplication
  • Division (correct)

A school has 525 students and wants to divide them equally into 15 classes. Which equation represents the number of students per class?

  • $525 \div 15 = []$ (correct)
  • $525 - 15 = []$
  • $525 \times 15 = []$
  • $525 + 15 = []$

If 455 avocados are to be divided equally into 13 groups, how many avocados will each group receive?

<p>35 avocados (D)</p> Signup and view all the answers

If the cost of 25 sweets is 750 shillings, what operation will determine the cost of one sweet?

<p>Division (A)</p> Signup and view all the answers

What is the result when 1,250 is divided by 25?

<p>40 (A)</p> Signup and view all the answers

A farmer harvests 1,548 mangoes and wants to pack them into boxes, with each box holding 36 mangoes. How many boxes are needed?

<p>43 (A)</p> Signup and view all the answers

When performing short division, what does the term 'quotient' represent?

<p>The result obtained after dividing one number by another. (A)</p> Signup and view all the answers

In the long division method, after dividing and multiplying, which step immediately follows?

<p>Subtracting to find the difference. (D)</p> Signup and view all the answers

In a division problem, if the dividend is not an exact multiple of the divisor, what will always be present?

<p>A remainder. (C)</p> Signup and view all the answers

Consider the division problem $452 \div 21$. Which of the following statements accurately describes the process and potential outcome?

<p>The quotient will be a whole number, and there might be a remainder if 452 is not exactly divisible by 21. (A)</p> Signup and view all the answers

What is the primary difference between the short division method and the long division method?

<p>Long division provides a more detailed, step-by-step approach, while short division is a condensed version. (C)</p> Signup and view all the answers

In the short division method, where is the quotient placed in relation to the divisor and dividend?

<p>Below the dividend and to the right of the divisor. (B)</p> Signup and view all the answers

When performing short division, in which direction should you proceed through the digits of the dividend?

<p>From left to right, carrying over remainders. (D)</p> Signup and view all the answers

If you are dividing 84,620 by 2 using short division, what is the first step?

<p>Divide 8 by 2 to get 4. (D)</p> Signup and view all the answers

In short division, what does it mean if a digit in the dividend cannot be evenly divided by the divisor?

<p>A remainder is carried over to the next digit. (D)</p> Signup and view all the answers

What should you do if dividing a '0' by any divisor in short division?

<p>Write '0' in the quotient above the '0'. (A)</p> Signup and view all the answers

Suppose you are dividing 735 by 5 using the short division method. After dividing 7 by 5, what would be the next step?

<p>Carry the remainder from 7 divided by 5 to the next digit, making it 23, then divide 23 by 5. (A)</p> Signup and view all the answers

What is the primary advantage of using the short division method compared to long division?

<p>It requires less writing and is quicker for simpler divisions. (D)</p> Signup and view all the answers

If a student correctly performs the short division of 693 by 3, what digits would they write under the dividend?

<p>231 (D)</p> Signup and view all the answers

When using short division, how do you handle a situation where the divisor is larger than the first digit of the dividend?

<p>Combine the first two digits of the dividend and divide that number by the divisor. (A)</p> Signup and view all the answers

What is the result of $84620 \div 2$?

<p>42310 (B)</p> Signup and view all the answers

In the provided examples, what is the primary arithmetic operation being demonstrated?

<p>Division (B)</p> Signup and view all the answers

Which of the following best describes the process of long division as exemplified in the text?

<p>Breaking down the dividend into smaller parts and dividing each by the divisor. (C)</p> Signup and view all the answers

What is the significance of obtaining a '0' after the final subtraction in a long division problem?

<p>It confirms that the division is exact with no remainder. (D)</p> Signup and view all the answers

If, during a long division calculation, the number to be subtracted is larger than the current partial dividend, what adjustment needs to be made?

<p>Decrease the quotient and bring down the next digit from the dividend. (A)</p> Signup and view all the answers

Consider a division problem where the dividend is 750 and the quotient is 25. Use your understanding of division to deduce the divisor.

<p>30 (D)</p> Signup and view all the answers

Which expression accurately represents the relationship between the dividend, divisor, quotient, and remainder in a division problem?

<p>Dividend = (Divisor × Quotient) + Remainder (B)</p> Signup and view all the answers

A student is performing long division and finds that after subtracting, the remaining number is larger than the divisor. What does this indicate?

<p>The quotient chosen for that step was too small. (B)</p> Signup and view all the answers

If you are dividing 9876 by 12, which part of the number 9876 would you initially focus on to begin the long division process?

<p>98 (A)</p> Signup and view all the answers

In a division exercise, a student mistakenly multiplies instead of divides. If the question was 150 ÷ 5, but the student calculates 150 x 5, what is the difference between their incorrect answer and the correct quotient?

<p>720 (B)</p> Signup and view all the answers

In long division, after bringing down a digit, the resulting number is still smaller than the divisor. What is the next step?

<p>Place a zero in the quotient and bring down the next digit. (C)</p> Signup and view all the answers

In the division problem of 14496 ÷ 32, after the first subtraction, what value is brought down to continue the division?

<p>6, from the ones place of 14496. (C)</p> Signup and view all the answers

During the long division of 14496 by 32, what is the significance of writing '5' in the quotient position?

<p>It shows that 32 goes into 169 approximately 5 times. (D)</p> Signup and view all the answers

In the given long division example, what does the subtraction of 160 from 169 represent?

<p>Subtracting the product of the divisor and the estimated quotient from the dividend. (D)</p> Signup and view all the answers

Why is the digit '3' placed to the right of the '5' in the quotient during the long division of 14496 by 32?

<p>To indicate that 32 divides evenly into the remainder from the previous step. (B)</p> Signup and view all the answers

What is the role of the number '96' in the long division process of 14496 by 32?

<p>It represents the portion of the dividend that still needs to be divided by 32 after the first step. (A)</p> Signup and view all the answers

In the long division of 14496 by 32, multiplying 32 by 5 results in 160. What does this calculation primarily help to determine?

<p>The approximate number of times 32 goes into the first three digits (144) of the dividend. (A)</p> Signup and view all the answers

What does the '0' at the end of the long division of 14496 by 32 signify?

<p>It confirms that the division is exact, and there is no remainder. (D)</p> Signup and view all the answers

If, during a similar division process, the result of subtracting the product of the divisor and quotient from the dividend yields a number larger than the divisor, what adjustment should be made?

<p>Increase your initial estimate of the quotient. (A)</p> Signup and view all the answers

In a long division problem, why is it essential to align the digits properly during each step of the subtraction process?

<p>To ensure that each digit represents its correct place value, which is crucial for accurate subtraction and carrying down of numbers. (A)</p> Signup and view all the answers

In a scenario where 2,550 items are equally divided among 25 groups, and then each group further divides their share equally among 5 subgroups, what is the number of items each subgroup receives?

<p>20 items (D)</p> Signup and view all the answers

A charity has collected 3,150 blankets to distribute equally among several refugee camps. If each camp is to receive 225 blankets, how many refugee camps will receive blankets?

<p>14 camps (C)</p> Signup and view all the answers

A printing company has 7,350 sheets of paper. They need to divide these sheets to print 35 copies of a report. How many sheets of paper does each copy of the report require?

<p>210 sheets (A)</p> Signup and view all the answers

A school is organizing a field trip and needs to divide 472 students into groups of 8 for supervision. Each group will also have 2 parent volunteers. How many total groups will there be for the field trip?

<p>59 groups (A)</p> Signup and view all the answers

In the division example where 61672 is divided by 696, what does the final result of '0' after subtraction indicate?

<p>The division is exact with no remainder. (C)</p> Signup and view all the answers

In the long division process illustrated, what is the significance of subtracting '8820' from '9780' in the example $978040 \div 980$?

<p>It determines the next digit of the quotient. (B)</p> Signup and view all the answers

A warehouse contains 9,450 boxes that need to be shipped. If each truck can carry 450 boxes, how many trucks are needed to transport all of the boxes?

<p>21 trucks (B)</p> Signup and view all the answers

If, while solving $49000 \div 7$, a student calculates the answer as 6000, what fundamental error might they have made?

<p>Incorrectly placing the zeroes during division. (C)</p> Signup and view all the answers

When dividing 26789 by 43, a student arrives at a two-digit quotient without a remainder. What could this imply about their calculation?

<p>A flawed division that needs verification. (C)</p> Signup and view all the answers

Suppose after dividing 980000 by 200, a student obtains 490 instead of 4900. What is the most probable mistake in their process?

<p>Dividing all digits correctly but missing a zero. (D)</p> Signup and view all the answers

During the division of a large number by 75, a student consistently underestimates each digit of the quotient. How would this affect the final result?

<p>The final remainder would be larger, and the quotient smaller, than they should be. (A)</p> Signup and view all the answers

In a division problem, if the divisor is 364 and the dividend is 22932, which step is crucial for accurately determining the first digit of the quotient?

<p>Focusing on dividing 2293 by 364 to properly estimate the quotient digit. (B)</p> Signup and view all the answers

When using short division, if the divisor does not divide evenly into a digit, what is typically done?

<p>Carry the remainder over to the next digit. (B)</p> Signup and view all the answers

In short division, after placing the first digit of the quotient, what determines the next step?

<p>Whether the previous division resulted in a remainder. (A)</p> Signup and view all the answers

In short division, what does it mean if, after dividing a digit in the dividend by the divisor, the result is '0'?

<p>The quotient for that digit is zero, and you proceed to the next digit. (B)</p> Signup and view all the answers

If you're using short division and find that the divisor is larger than the group of digits you're currently dividing, what should you do?

<p>Write '0' as the quotient for that place value and carry all the digits to the next place value. (D)</p> Signup and view all the answers

In the short division method, how do you handle a zero in the dividend?

<p>Write a '0' in the quotient above the zero in the dividend and proceed. (D)</p> Signup and view all the answers

What does the arrangement of dividend, divisor, and quotient look like in short division?

<p>Divisor to the left, dividend to the right, quotient below. (B)</p> Signup and view all the answers

Suppose you are dividing 575 by 5 using short division. After dividing 5 by 5 and writing '1' in the quotient, what is the next immediate step?

<p>Divide 7 by 5 and write the result in the quotient. (C)</p> Signup and view all the answers

If you're dividing 315 by 5 using short division correctly, which digits would you write under the dividend?

<p>63 (A)</p> Signup and view all the answers

In the example of $27\overline{)866}$ shown, after multiplying 27 by 32, what is the significance of subtracting the result from 866?

<p>To find the remainder of the division. (A)</p> Signup and view all the answers

In the division of 148 by 7, what does writing '2' above the tens position signify?

<p>It represents the number of times 7 goes into 14. (A)</p> Signup and view all the answers

In the division of 148 by 7, after subtracting 14 from 14, why is the 8 'dropped' down?

<p>To continue the division using the next digit of the dividend. (D)</p> Signup and view all the answers

In the example $27\overline{)866}$, what does the '32' above the 866 represent?

<p>The quotient (B)</p> Signup and view all the answers

If, after performing several steps of long division, you find that the remaining number is larger than the divisor, what does this indicate?

<p>The quotient digit is too small and needs to be increased. (A)</p> Signup and view all the answers

What does a remainder of 1 in the division of 148 by 7 indicate?

<p>After dividing as much as possible, 1 is left over. (C)</p> Signup and view all the answers

In the long division process exemplified by $27\overline{)866}$, how does multiplying the divisor (27) by a digit of the quotient (e.g., 32) help in solving the problem?

<p>It determines how much to subtract from the current portion of the dividend. (D)</p> Signup and view all the answers

In dividing 148 by 7, after subtracting 14 from 14 and dropping down 8, why divide 8 by 7?

<p>To determine the next digit of the quotient. (D)</p> Signup and view all the answers

Why is it important to write the digits of the quotient in the correct place value columns above the dividend?

<p>To ensure correct multiplication of the divisor and quotient, and proper representation of the final answer. (A)</p> Signup and view all the answers

What is the relationship between the dividend, divisor, quotient, and remainder in division?

<p>(Divisor x Quotient) + Remainder = Dividend (A)</p> Signup and view all the answers

In the division problem $12 \overline{)573}$, why is the initial step to divide 57 by 12 instead of just 5 by 12?

<p>Because 5 is not large enough to be divided by 12, so you must consider the next digit to form a larger number. (A)</p> Signup and view all the answers

When dividing 93 by 12, which results in a quotient of 7 and a remainder of 9, what does the quotient '7' represent in the context of the original problem $12 \overline{)573}$?

<p>The number of times 12 goes into 93, which is derived after combining the remainder from the previous division with the next digit. (A)</p> Signup and view all the answers

If you are dividing 678 by 10, and you find that 10 goes into 67 six times, what is the next step in the division process?

<p>Subtract 60 from 67, bring down the 8, and continue dividing. (C)</p> Signup and view all the answers

In the problem $12 \overline{)573}$, the solution states '47 remainder 9'. How can you check if this result is correct?

<p>Multiply 12 by 47 and add 9; the result should equal 573. (C)</p> Signup and view all the answers

When solving $3 \overline{)457}$, what is the first step in the division process?

<p>Divide 4 by 3. (C)</p> Signup and view all the answers

If dividing 99 by 5, you would find that 5 goes into 9 once with a remainder. What do you do with this remainder?

<p>Combine the remainder with the next digit in the dividend to form a new number to divide. (D)</p> Signup and view all the answers

When dividing 644 by 10, after determining that 10 goes into 64 six times, what arithmetic operation is performed next?

<p>Subtraction (C)</p> Signup and view all the answers

In the context of division, what does it mean to have a 'remainder'?

<p>The amount left over when one number cannot be divided exactly by another. (D)</p> Signup and view all the answers

How does understanding remainders in division help in real-life situations?

<p>It helps in distributing items equally and understanding what is leftover. (C)</p> Signup and view all the answers

Why is it important to write the digits of the quotient in the correct place value column during division?

<p>To ensure accurate representation of the value and maintain the correct magnitude of the final answer. (B)</p> Signup and view all the answers

In the example division problem $696 \overline{)561672}$, what does the '807' represent?

<p>The quotient. (B)</p> Signup and view all the answers

In the long division example $980 \overline{)978040}$, what is the result of the first subtraction (9780 - 8820)?

<p>9604 (D)</p> Signup and view all the answers

In the example $980 \overline{)978040}$, what does the final subtraction resulting in '0' signify?

<p>The dividend is completely divisible by the divisor. (A)</p> Signup and view all the answers

If you're solving $7 \overline{)49000}$ and get a quotient of 700, what potential error did you make?

<p>Forgetting to include the zeros. (B)</p> Signup and view all the answers

If a student is dividing 26789 by 43 and the resulting quotient is a two-digit number, what does this imply?

<p>The student may have made a mistake and should check the calculation. (A)</p> Signup and view all the answers

During the long division of 980000 by 200, a student mistakenly obtains 490 instead of 4900. What is the most probable mistake in their process?

<p>Omitting a zero in the quotient. (D)</p> Signup and view all the answers

You are dividing a large number by 75. If you consistently underestimate each digit of the quotient, how would this affect the final result?

<p>The quotient will be smaller than the correct value. (B)</p> Signup and view all the answers

A store has 2,550 pens to be distributed equally among 25 schools. Each school then divides its share equally among 6 classes. How many pens does each class receive?

<p>17 pens (D)</p> Signup and view all the answers

A company transports 4,275 laptops and wants to distribute them among several branches. If each branch is to receive 125 laptops, how many branches will receive the laptops?

<p>34 branches (B)</p> Signup and view all the answers

A factory produces 9,450 candies that need to be packed into boxes, with an average of 75 candies per box, intended for 18 different stores. How many boxes will each store receive?

<p>7 boxes (A)</p> Signup and view all the answers

A stationery shop has 5,346 pencils and wants to group them into sets of 12 for resale. After making as many complete sets as possible, the remaining pencils will be sold individually. How many pencils will be sold individually?

<p>6 pencils (A)</p> Signup and view all the answers

In a division problem, if the dividend is 8,765 and the quotient is 625, what is the closest whole number for the divisor, and what is the remainder?

<p>Divisor: 14, Remainder: 15 (C)</p> Signup and view all the answers

In short division, after dividing the 'hundreds' digit, what digit of the dividend do you operate on next?

<p>Tens (A)</p> Signup and view all the answers

What does the placement of the quotient directly below the dividend in short division primarily facilitate?

<p>Clear tracking of digit-by-digit division results. (B)</p> Signup and view all the answers

In short division, if the divisor cannot divide evenly into the current digit of the dividend, what happens to the remainder?

<p>It's carried over to the next digit of the dividend. (C)</p> Signup and view all the answers

Suppose you're using short division to divide 936 by 3. After successfully dividing the '9' in the hundreds place, what is your immediate next calculation?

<p>Divide 3 (from the tens place) by 3. (B)</p> Signup and view all the answers

If you are dividing 642 by 2 using short division, and you've already determined that 2 goes into 6 three times, what is the very next step?

<p>Divide 4 by 2. (A)</p> Signup and view all the answers

In the context of short division, what does a '0' in the quotient signify when dividing a specific digit of the dividend?

<p>The divisor is larger than the current digit being divided. (C)</p> Signup and view all the answers

When performing short division, what does it signify if after dividing a digit you get a remainder?

<p>The remainder must be carried over to the next digit. (C)</p> Signup and view all the answers

What adjustment is required if, during short division, you find that the divisor is greater than the digit you are trying to divide?

<p>Place a '0' in the quotient and combine the current digit with the next digit of the dividend. (D)</p> Signup and view all the answers

Imagine you are using the short division method to divide 567 by 7. After correctly performing the division, what is the resulting quotient?

<p>81 (B)</p> Signup and view all the answers

In the long division example of 27 into 866, after multiplying 27 by 2, why is the result (54) subtracted from 56?

<p>To reduce the dividend to a manageable size for the next division step. (A)</p> Signup and view all the answers

In the long division of 148 by 7, what does writing the '2' above the tens position signify?

<p>7 goes into 14 (the tens and hundreds digits of 148) two times. (A)</p> Signup and view all the answers

When performing long division on 148 7, after subtracting 14 from 14, why is the 8 'dropped' down next to the result?

<p>To include all digits of the dividend in the division process. (D)</p> Signup and view all the answers

In the example division problem $27 \overline{)866}$, the '32' written above 866 represents which of the following?

<p>The quotient of the division. (B)</p> Signup and view all the answers

What does a remainder of 1 in the division problem 148 7 signify?

<p>After dividing as much as possible, 1 is left over. (D)</p> Signup and view all the answers

In the long division process exemplified by $27 \overline{)866}$, how does multiplying the divisor (27) by a trial digit of the quotient (like 32) help solve the problem?

<p>It estimates how many times the divisor fits into part of the dividend. (C)</p> Signup and view all the answers

In dividing 148 by 7, after subtracting 14 from 14 and dropping down 8, why is the next step to divide 8 by 7?

<p>To determine how many times 7 goes into the remaining part of the dividend. (B)</p> Signup and view all the answers

Why is it important to write the digits of the quotient in the correct place value columns above the dividend during long division?

<p>To keep track of the value each digit in the quotient represents. (D)</p> Signup and view all the answers

In the division problem $12 \overline{)573}$, what does the '4' in the quotient '47 remainder 9' represent?

<p>The number of times 12 goes into 57 tens. (C)</p> Signup and view all the answers

If you have divided 678 by 10 and found that 10 goes into 67 six times, what is a crucial next step in solving this problem?

<p>Subtract 60 (6 x 10) from 67 to find the remainder and continue the division. (D)</p> Signup and view all the answers

In the division problem $3 \overline{)457}$, what is the initial step in the division process, and why?

<p>Divide 4 by 3, focusing on the leftmost digit first. (A)</p> Signup and view all the answers

What is the correct interpretation of a remainder when dividing 99 by 5?

<p>The remainder represents the amount 'left over' that couldn't be evenly divided. (C)</p> Signup and view all the answers

You are dividing 644 by 10. After determining that 10 goes into 64 six times, which of the following operations do you perform next?

<p>Subtract 60 (6 x 10) from 64. (B)</p> Signup and view all the answers

Which situation best illustrates the usefulness of understanding remainders in division?

<p>Determining how many full teams can be formed from a group and how many people are left without a team. (C)</p> Signup and view all the answers

Why is placing the digits of the quotient in the correct place value column essential during division?

<p>It ensures that the value represented by each digit in the quotient is correctly accounted for, maintaining the accuracy of the result. (A)</p> Signup and view all the answers

In the division problem $12 \overline{)573}$, why is the initial focus on dividing 57 by 12 rather than just 5 by 12?

<p>12 is not divisible by 5, so you consider the first two digits together to find a number that 12 can divide into. (A)</p> Signup and view all the answers

When dividing 93 by 12, the result is a quotient of 7 and a remainder of 9. In the context of the original problem $12 \overline{)573}$, what does this quotient '7' specifically represent?

<p>The number of times 12 goes into the remaining 93 after initially dividing 57 by 12. (C)</p> Signup and view all the answers

You're solving $12 \overline{)573}$ and arrive at a solution of '47 remainder 9'. How could you verify if this result is accurate?

<p>Multiply the quotient by the divisor and add the remainder; the result should equal the dividend. (D)</p> Signup and view all the answers

Division is a mathematical process of distributing things into a specified number of parts.

<p>True (A)</p> Signup and view all the answers

In Standard Four, students learned about division of numbers having a maximum of four digits.

<p>False (B)</p> Signup and view all the answers

In this chapter, students will learn how to divide a number not exceeding one million by a divisor having up to three digits.

<p>True (A)</p> Signup and view all the answers

A knowledge of division can assist in tasks like budgeting and resource allocation.

<p>True (A)</p> Signup and view all the answers

Arranging 408 books into six groups results in each group containing 58 books.

<p>False (B)</p> Signup and view all the answers

If eighteen sweets are divided equally among 3 children, each child gets 6 sweets.

<p>True (A)</p> Signup and view all the answers

If 28 avocados are divided equally into 14 groups, each group will have 4 avocados.

<p>False (B)</p> Signup and view all the answers

The method of repeated subtraction can be used for division.

<p>True (A)</p> Signup and view all the answers

In division, the number that is divided is called the 'divisor'.

<p>False (B)</p> Signup and view all the answers

The result of a division problem is called the 'quotient'.

<p>True (A)</p> Signup and view all the answers

In the example $2522 \div 97 = 26$, the number 97 is the dividend.

<p>False (B)</p> Signup and view all the answers

When using long division, the divisor is placed inside the division symbol.

<p>False (B)</p> Signup and view all the answers

The first step in the provided long division example is to divide 144 by 32.

<p>True (A)</p> Signup and view all the answers

When subtracting in long division, you write the result above the dividend.

<p>False (B)</p> Signup and view all the answers

After subtracting 128 from 144 in the example, the remainder is 26.

<p>False (B)</p> Signup and view all the answers

In long division, you bring down the next digit to the right of the remainder.

<p>True (A)</p> Signup and view all the answers

When dividing 169 by 32, the first digit of the quotient is placed to the far left.

<p>False (B)</p> Signup and view all the answers

When dividing 14496 by 32, the result is 453.

<p>True (A)</p> Signup and view all the answers

When dividing 169 by 32, the result is 5 with a remainder of 9.

<p>True (A)</p> Signup and view all the answers

After subtracting 160 from 169, you bring down the number 9.

<p>False (B)</p> Signup and view all the answers

To begin the process, divide 32 by 169.

<p>False (B)</p> Signup and view all the answers

The final remainder after dividing 14496 by 32 is 96.

<p>False (B)</p> Signup and view all the answers

When dividing 96 by 32, you get a quotient of 4 with no remainder.

<p>False (B)</p> Signup and view all the answers

The short division method is always used to find the remainder in division problems.

<p>False (B)</p> Signup and view all the answers

Writing 160 below 169 is part of the multiplication step.

<p>True (A)</p> Signup and view all the answers

In the division problem, the number being divided is called the divisor.

<p>False (B)</p> Signup and view all the answers

In division, the dividend is always a multiple of the divisor.

<p>False (B)</p> Signup and view all the answers

After bringing down the 6, the next step is to divide 96 by 32.

<p>True (A)</p> Signup and view all the answers

The quotient is the result obtained after dividing one number by another.

<p>True (A)</p> Signup and view all the answers

Long division involves subtracting multiples of the divisor from the dividend to find the quotient.

<p>True (A)</p> Signup and view all the answers

In long division, you write the result of multiplying the divisor by a digit of the quotient above the dividend.

<p>False (B)</p> Signup and view all the answers

In short division, the divisor is placed inside the division symbol.

<p>False (B)</p> Signup and view all the answers

The quotient is the result of a division.

<p>True (A)</p> Signup and view all the answers

When dividing, always start from right to left.

<p>False (B)</p> Signup and view all the answers

If you divide 84,620 by 2, the ten thousands digit in the result is 4.

<p>True (A)</p> Signup and view all the answers

Zero divided by any number is always zero.

<p>True (A)</p> Signup and view all the answers

The dividend is the number that divides another number.

<p>False (B)</p> Signup and view all the answers

In division, remainders are never possible.

<p>False (B)</p> Signup and view all the answers

Ten thousands come directly after thousands in place value.

<p>True (A)</p> Signup and view all the answers

2 divided by 84,620 is 42,315.

<p>False (B)</p> Signup and view all the answers

The final step in the example is to divide the tens digit by 2.

<p>False (B)</p> Signup and view all the answers

Division is a mathematical operation that combines multiple groups into a single larger group.

<p>False (B)</p> Signup and view all the answers

If 36 sweets are divided equally among 4 children, each child will receive 8 sweets.

<p>False (B)</p> Signup and view all the answers

If 42 mangoes are divided equally into 21 groups, each group will contain 2 mangoes.

<p>True (A)</p> Signup and view all the answers

If a school has 360 students and 15 classrooms and the students are equally distributed, each class will have 24 students.

<p>True (A)</p> Signup and view all the answers

If the cost of 10 pencils is 150 shillings, then the cost of one pencil is 20 shillings.

<p>False (B)</p> Signup and view all the answers

In division, a remainder is always greater than the divisor.

<p>False (B)</p> Signup and view all the answers

Dividing 7,536 by 12 results in a quotient of 628.

<p>True (A)</p> Signup and view all the answers

Repeated subtraction can be used as a method to solve division problems.

<p>True (A)</p> Signup and view all the answers

In the expression $72 \div 8 = 9$, the number 8 is called the dividend.

<p>False (B)</p> Signup and view all the answers

When performing long division, the divisor is placed to the left of the dividend.

<p>True (A)</p> Signup and view all the answers

In the division problem $15 \div 5 = 3$, the quotient is 5.

<p>False (B)</p> Signup and view all the answers

If after a long division calculation, there's a non-zero number left, that number is called the remainder.

<p>True (A)</p> Signup and view all the answers

Using repeated subtraction to solve $30 \div 6$, you would subtract 6 from 30 a total of 6 times.

<p>False (B)</p> Signup and view all the answers

When dividing 155 by 5 using long division, the first step is to determine how many times 15 goes into 5.

<p>False (B)</p> Signup and view all the answers

The dividend is the number you are dividing by.

<p>False (B)</p> Signup and view all the answers

In long division, after bringing down a digit, if the resulting number is still smaller than the divisor, you write a '1' in the quotient.

<p>False (B)</p> Signup and view all the answers

In short division, if dividing 95 by 7, the first step involves dividing 9 by 7, resulting in a quotient of 1, and carrying over 5 as the remainder.

<p>False (B)</p> Signup and view all the answers

When performing short division on the number 125 divided by 5, the last step involves dividing 25 by 5.

<p>True (A)</p> Signup and view all the answers

When using short division to divide 156 by 3, the initial step involves dividing 15 by 3.

<p>False (B)</p> Signup and view all the answers

In the short division method, remainders from previous division steps are ignored in subsequent steps.

<p>False (B)</p> Signup and view all the answers

When dividing 148 by 7 using short division, the quotient will always be a three-digit number.

<p>False (B)</p> Signup and view all the answers

In long division, the initial step involves multiplying the divisor by the first digit of the dividend.

<p>False (B)</p> Signup and view all the answers

When a remainder is smaller than the divisor, we can proceed by bringing down the next digit from the dividend.

<p>True (A)</p> Signup and view all the answers

In the provided example, after subtracting 5568 from 5616, the remainder is correctly calculated as 48.

<p>True (A)</p> Signup and view all the answers

If dividing a number by 696 results in a quotient of 807 with no remainder, multiplying 696 by 807 will yield the original number.

<p>True (A)</p> Signup and view all the answers

In the example, writing '0' in the quotient after bringing down a digit implies the divisor goes into the new number exactly once.

<p>False (B)</p> Signup and view all the answers

The quotient obtained in the provided long division example is 87.

<p>False (B)</p> Signup and view all the answers

When performing long division, it is acceptable to have a remainder that is larger than the divisor.

<p>False (B)</p> Signup and view all the answers

In the calculation, after bringing down the '7', the new dividend portion, 487, is divided by 696, resulting in a quotient of 1.

<p>False (B)</p> Signup and view all the answers

In long division, if at any stage the result of the subtraction is zero, you must proceed by bringing down the next digit from the dividend.

<p>True (A)</p> Signup and view all the answers

In the given example, the dividend is 696 and the divisor is 561672.

<p>False (B)</p> Signup and view all the answers

In the example provided, 696 multiplied by 7 equals 4872.

<p>True (A)</p> Signup and view all the answers

In the division example in the text, the quotient of 978040 divided by 980 is exactly 998.72.

<p>False (B)</p> Signup and view all the answers

Based on the calculations shown, subtracting 4872 from 4872 results in 487.

<p>False (B)</p> Signup and view all the answers

When performing long division, the remainder must always be a non-negative number.

<p>True (A)</p> Signup and view all the answers

In the exercise questions provided, every problem involves division with two whole numbers.

<p>True (A)</p> Signup and view all the answers

If 29190 is divided by 10, according to the exercises, the result will be 2920.

<p>False (B)</p> Signup and view all the answers

The expression 7 49000 represents $49000 imes 7$.

<p>False (B)</p> Signup and view all the answers

The quotient of 26789 divided by 43 will have no decimal places.

<p>False (B)</p> Signup and view all the answers

In the long division examples, the dividend is always smaller than the divisor.

<p>False (B)</p> Signup and view all the answers

Based on the context, the expression 200 980000 means that 200 is multiplied by 980000.

<p>False (B)</p> Signup and view all the answers

Which of the following options correctly translates the Roman numeral 'CDXLVII' into standard numerical form?

<p>447 (D)</p> Signup and view all the answers

What is the correct Roman numeral representation of the number 374?

<p>CCCLXXIV (B)</p> Signup and view all the answers

If you combine the values of 'CM' and 'IX', what number do you get?

<p>909 (D)</p> Signup and view all the answers

Which of the following Roman numerals represents the largest numerical value?

<p>CM (A)</p> Signup and view all the answers

How should the number 442 be represented using Roman numerals?

<p>CDXLII (A)</p> Signup and view all the answers

Which of the following Roman numerals represents the number 46?

<p>XLVI (B)</p> Signup and view all the answers

What number does the Roman numeral 'LXXX' represent?

<p>80 (D)</p> Signup and view all the answers

Which statement accurately describes how Roman numerals are combined to form numbers?

<p>Smaller values to the left are subtracted from larger values. (A)</p> Signup and view all the answers

What is the largest number of times that the same Roman numeral (I, X, or C) can be repeated consecutively when adding values?

<p>Three (D)</p> Signup and view all the answers

Convert the number 90 into Roman numerals.

<p>XC (A)</p> Signup and view all the answers

Which of the following correctly applies the subtraction rule in Roman numerals?

<p>XL = 40 (D)</p> Signup and view all the answers

What is the value of the Roman numeral XCIX?

<p>99 (A)</p> Signup and view all the answers

Which of the following represents the number 54 in Roman numerals?

<p>LIV (D)</p> Signup and view all the answers

What is the numerical equivalent of the Roman numeral LXXII?

<p>72 (C)</p> Signup and view all the answers

What number is represented by the Roman numeral LXIV?

<p>64 (A)</p> Signup and view all the answers

What value does the Roman numeral XCV represent?

<p>95 (D)</p> Signup and view all the answers

In Roman numerals, what is the value of LVIII?

<p>58 (C)</p> Signup and view all the answers

What numeral does LXI represent?

<p>61 (A)</p> Signup and view all the answers

Which of the following correctly converts the Roman numeral 'CXVII' into a numeral?

<p>117 (B)</p> Signup and view all the answers

What numeral is represented by the Roman numeral 'CDXLVI'?

<p>446 (C)</p> Signup and view all the answers

What is the correct numeral conversion of the Roman numeral 'CIV'?

<p>104 (A)</p> Signup and view all the answers

Which numeral corresponds to the Roman numeral 'CXIX'?

<p>119 (C)</p> Signup and view all the answers

The Roman numeral 'CLXXVI' represents which numeral?

<p>176 (D)</p> Signup and view all the answers

What numeral is denoted by the Roman numeral 'CCXXII'?

<p>222 (C)</p> Signup and view all the answers

Which of the following numerals is represented by the Roman numeral 'CCCXLIII'?

<p>343 (A)</p> Signup and view all the answers

The Roman numeral 'CCLIV' corresponds to which numeral?

<p>254 (B)</p> Signup and view all the answers

Which numeral is equivalent to the Roman numeral 'CDXXXI'?

<p>431 (A)</p> Signup and view all the answers

Which of the following correctly represents 93 in Roman numerals?

<p>XCIII (B)</p> Signup and view all the answers

What is 66 expressed as a Roman numeral?

<p>LXVI (A)</p> Signup and view all the answers

How is 'Seventy-five' written using Roman numerals?

<p>LXXV (A)</p> Signup and view all the answers

Which of the following Roman numerals represents 81?

<p>LXXXI (B)</p> Signup and view all the answers

In the series I, V, X, L, C... what number does 'L' represent?

<p>50 (B)</p> Signup and view all the answers

If arranging the Roman numerals C, I, X, L, V in ascending order, which would come second?

<p>V (C)</p> Signup and view all the answers

What number does 'CD' represent in the Roman numeral system?

<p>400 (D)</p> Signup and view all the answers

Which Roman numeral represents 205?

<p>CCV (A)</p> Signup and view all the answers

Which of the following shows the correct conversion of 362 into Roman Numerals?

<p>CCCLXII (C)</p> Signup and view all the answers

Which of these options correctly expresses the number 'One hundred' in Roman numerals?

<p>C (D)</p> Signup and view all the answers

Which of the following is NOT a typical application of Roman numerals?

<p>Representing quantities in algebraic equations (C)</p> Signup and view all the answers

What value is represented by the Roman numeral 'XLIX'?

<p>49 (B)</p> Signup and view all the answers

If a classroom is labeled 'Classroom XXXIV', what number does this represent?

<p>34 (A)</p> Signup and view all the answers

What is the Arabic numeral equivalent of the Roman numeral 'XXIV'?

<p>24 (D)</p> Signup and view all the answers

Which Roman numeral represents the number 38?

<p>XXXVIII (B)</p> Signup and view all the answers

Which of the provided Roman numerals has the lowest value?

<p>DLXIV (B)</p> Signup and view all the answers

Express 950 using Roman numerals.

<p>CML (A)</p> Signup and view all the answers

What Arabic number is represented by the sum of XCI and CCCXIV?

<p>305 (D)</p> Signup and view all the answers

Which of these numbers cannot be correctly represented by repeating a Roman numeral more than three times?

<p>40 (B)</p> Signup and view all the answers

Which of the following correctly represents the number 65 in Roman numerals?

<p>LXV (D)</p> Signup and view all the answers

If a Roman numeral is written to the left of a larger number, what operation does this imply?

<p>Subtraction (C)</p> Signup and view all the answers

Express the number 76 in Roman numerals.

<p>LXXVI (B)</p> Signup and view all the answers

Which of the following is an invalid representation of a Roman numeral, according to the rules?

<p>VIIII (B)</p> Signup and view all the answers

What is the result of adding X and L in Roman numerals?

<p>LX (A)</p> Signup and view all the answers

In Roman numerals, if 'IV' is written to the right of a larger number, what operation is applied?

<p>Addition (C)</p> Signup and view all the answers

The Roman numeral 'XCV' translates to what number?

<p>95 (C)</p> Signup and view all the answers

Which of the following Roman numerals represents seventy-two?

<p>LXXII (D)</p> Signup and view all the answers

In Roman numerals, what is the representation of sixty-one?

<p>LXI (A)</p> Signup and view all the answers

What does the Roman numeral 'LXXXV' stand for?

<p>85 (B)</p> Signup and view all the answers

Which Roman numeral corresponds to the number seventy-three?

<p>LXXIII (D)</p> Signup and view all the answers

What is the Roman numeral representation of 93?

<p>XCIII (C)</p> Signup and view all the answers

Which of the following is the correct Roman numeral for seventy-five?

<p>LXXV (B)</p> Signup and view all the answers

Arrange I, V, X in ascending order.

<p>I, V, X (D)</p> Signup and view all the answers

Which Roman numeral comes immediately after LXXX in the given pattern: LXXX, _____, LXXXII, _____, LXXXIV, _____?

<p>LXXXI (D)</p> Signup and view all the answers

What number does 'CC' represent in numerals?

<p>200 (B)</p> Signup and view all the answers

What is 300 in Roman numerals?

<p>CCC (C)</p> Signup and view all the answers

What is the number representing CD in numerals?

<p>400 (D)</p> Signup and view all the answers

Roman numbers are not used to show hours on some analogue clocks.

<p>False (B)</p> Signup and view all the answers

The Roman numeral 'M' corresponds to the Arabic number 1000.

<p>True (A)</p> Signup and view all the answers

Roman numerals are sometimes used for ranking items, using symbols like I, II, and III.

<p>True (A)</p> Signup and view all the answers

The Roman number L represents the Arabic number 100.

<p>False (B)</p> Signup and view all the answers

The Roman numeral 'V' represents the number 10.

<p>False (B)</p> Signup and view all the answers

Writing preliminaries is one place that Roman numerals are used.

<p>True (A)</p> Signup and view all the answers

The Roman number XLIX equals the Arabic number 59.

<p>False (B)</p> Signup and view all the answers

The Roman numeral 'I' corresponds to the number 5.

<p>False (B)</p> Signup and view all the answers

In Roman numerals, when a smaller number is written to the left of a larger number, it is subtracted.

<p>True (A)</p> Signup and view all the answers

The Roman numeral LXXVI represents the number 86.

<p>False (B)</p> Signup and view all the answers

In Roman numerals, a number can be repeated infinitely to the right of a greater number.

<p>False (B)</p> Signup and view all the answers

The roman number V can be repeated when writen to the left of a greater number.

<p>False (B)</p> Signup and view all the answers

In Roman numerals, CMIX is equal to 909.

<p>True (A)</p> Signup and view all the answers

The Roman numeral DCCLXXIV represents the number 774.

<p>True (A)</p> Signup and view all the answers

DXL in Roman numerals represents five hundred and eleven.

<p>True (A)</p> Signup and view all the answers

CMLXXXIV represents nine hundred and eighty-four.

<p>True (A)</p> Signup and view all the answers

The Roman numeral DL represents six hundred and fifty.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CXVII represents the number 117.

<p>True (A)</p> Signup and view all the answers

CIV in Roman numerals represents the number 106.

<p>False (B)</p> Signup and view all the answers

CXIX in Roman Numerals represents 119.

<p>True (A)</p> Signup and view all the answers

CLXXVI represents the number 166.

<p>False (B)</p> Signup and view all the answers

CCCXLIII in Roman numerals is equal to 343.

<p>True (A)</p> Signup and view all the answers

The Roman numeral for 52 is LII.

<p>True (A)</p> Signup and view all the answers

CCXXV in Roman numerals represents 235.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CCCXXXVIII represents the number 338.

<p>True (A)</p> Signup and view all the answers

CDXVII represents the number 517.

<p>False (B)</p> Signup and view all the answers

The Roman numeral for fifty-one is IL.

<p>False (B)</p> Signup and view all the answers

The Roman numeral for sixty-three is LXII.

<p>False (B)</p> Signup and view all the answers

The Roman numeral for seventy-five is LXXV.

<p>True (A)</p> Signup and view all the answers

The Roman numeral for eighty-four is LXXXIV.

<p>True (A)</p> Signup and view all the answers

The Roman numeral for ninety-two is LXXXXII.

<p>False (B)</p> Signup and view all the answers

Roman numerals are exclusively used for academic purposes like naming classrooms and class levels.

<p>False (B)</p> Signup and view all the answers

The number 49 can be correctly written as 'IL' in Roman numerals.

<p>False (B)</p> Signup and view all the answers

The number 14 is represented as 'XIV', where 'X' stands for 10 and 'IV' stands for 4.

<p>True (A)</p> Signup and view all the answers

The Roman numeral for 38 is 'XXXIIX'.

<p>False (B)</p> Signup and view all the answers

The value of 'XXXIII' is thirty-three.

<p>True (A)</p> Signup and view all the answers

The numerical value of 'XLIX' in Arabic numbers is 69.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CMIX represents the number 909.

<p>True (A)</p> Signup and view all the answers

The Roman numeral DCCLXXIV is equivalent to 784.

<p>False (B)</p> Signup and view all the answers

The Roman numeral DCLXXIV represents the number six hundred and seventy four.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CMXXVII represents the number nine hundred and thirty-seven.

<p>False (B)</p> Signup and view all the answers

The Roman Numeral DL represents the number five hundred and fifty.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CXVII is equivalent to the number 117.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CDXLVI represents the number 446.

<p>True (A)</p> Signup and view all the answers

The numerical representation of the Roman numeral CIV is 106.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CXIX corresponds to the number 119.

<p>True (A)</p> Signup and view all the answers

CLXXVI in Roman numerals is equal to 186.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CCXXII translates to the number 222.

<p>True (A)</p> Signup and view all the answers

The number 343 can be written as CCXLIII in Roman numerals.

<p>False (B)</p> Signup and view all the answers

225 is represented as CCXXV in Roman numerals.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CCCXXXVIII is equivalent to 338.

<p>True (A)</p> Signup and view all the answers

In ascending order, the correct sequence of Roman numerals is: I, V, X, L, C.

<p>True (A)</p> Signup and view all the answers

The missing Roman numerals in the pattern LXXX, _____, LXXXII, _____, LXXXIV, _____ are LXXXI, LXXXIII, LXXXV.

<p>True (A)</p> Signup and view all the answers

The number 362 can be written as CCCLLXII in Roman numerals.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CD represents six hundred.

<p>False (B)</p> Signup and view all the answers

The Roman numeral CCV represents 205.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CCCXXX represents the number 330.

<p>True (A)</p> Signup and view all the answers

The Roman numeral CCXCII represents the number 292.

<p>True (A)</p> Signup and view all the answers

The number 444 can be written as CDLIV in Roman numerals.

<p>False (B)</p> Signup and view all the answers

The number 500 is represented by the Roman numeral M.

<p>False (B)</p> Signup and view all the answers

The number 100 can be written as IC in Roman numerals.

<p>False (B)</p> Signup and view all the answers

The number 209 is represented by the Roman numeral CCIX.

<p>True (A)</p> Signup and view all the answers

Which of the following sets contains only even numbers?

<p>30, 32, 34, 36 (C)</p> Signup and view all the answers

Which number is an even number that, when divided by 4, results in a whole number?

<p>20 (D)</p> Signup and view all the answers

In a sequence of consecutive even numbers, if the first number is 46 and the fourth number is 52, what is the second number in the sequence?

<p>48 (C)</p> Signup and view all the answers

Which of the following numbers will have a remainder when divided by 2?

<p>51 (A)</p> Signup and view all the answers

If you arrange 27 counters in groups of two, how many counters will be left over?

<p>1 (C)</p> Signup and view all the answers

What is the next odd number after 65?

<p>67 (B)</p> Signup and view all the answers

Which set of numbers includes only odd numbers?

<p>1, 3, 5, 7 (C)</p> Signup and view all the answers

Which option lists only odd numbers divisible by 3?

<p>3, 9, 15 (D)</p> Signup and view all the answers

Between 11 and 23, how many odd numbers are there?

<p>6 (A)</p> Signup and view all the answers

Which of the following is NOT a characteristic of even numbers, based on the described method of identification?

<p>They are always greater than odd numbers. (A)</p> Signup and view all the answers

Consider the sequence: 102, 106, 110, __, __. What are the next two even numbers in this increasing sequence?

<p>112, 114 (C)</p> Signup and view all the answers

Given a decreasing pattern of even numbers: 256, 252, 248, what is a potential rule and the next number in this sequence?

<p>Subtract 4; 244 (D)</p> Signup and view all the answers

Which set contains only even numbers?

<p>{2, 4, 6, 8} (C)</p> Signup and view all the answers

A store owner wants to arrange 75 items in pairs. How can one determine if an item will be left unpaired, and what does it indicate about the number 75?

<p>Divide 75 by 2; it is an odd number. (B)</p> Signup and view all the answers

If 'n' is an even number, which of the following expressions will always result in another even number?

<p>$n * 2$ (A)</p> Signup and view all the answers

Which of the following pairs of numbers are both even and sum up to 100?

<p>44 and 56 (A)</p> Signup and view all the answers

When finding the Least Common Multiple (LCM) using prime factor divisors, what indicates that the process is complete?

<p>When all numbers in the division process reach 1. (D)</p> Signup and view all the answers

In calculating the LCM of two numbers using the prime factor divisor method, if a prime number divides one of the numbers but not the other, what should you do?

<p>Divide only the number divisible by that prime number and carry down the other number unchanged. (A)</p> Signup and view all the answers

If the prime factor divisor method is used to find the LCM of 15 and 25, which of the following sequences of divisors would be correct?

<p>3, 5, 5 (C)</p> Signup and view all the answers

What is the purpose of finding the Least Common Multiple (LCM) of two or more numbers?

<p>To find the smallest number that each of the given numbers divides into evenly. (B)</p> Signup and view all the answers

Consider finding the LCM of 6, 15, and 20 using the prime factor divisor method. After dividing by 2, what numbers would you be working with in the next step?

<p>3, 15, 10 (A)</p> Signup and view all the answers

Why is the number 1 not considered a prime number?

<p>It only has one factor, itself. (D)</p> Signup and view all the answers

Which of the following is a prime number?

<p>23 (D)</p> Signup and view all the answers

If you are listing numbers from 1 to 50 to identify primes, after you've marked multiples of 2, 3, and 5, what is the next number whose multiples you would mark?

<p>7 (C)</p> Signup and view all the answers

How many prime numbers are there between 1 and 20, inclusive?

<p>8 (A)</p> Signup and view all the answers

In the process of identifying prime numbers up to 100, why do we encircle the prime number itself before marking its multiples?

<p>To exclude it from being marked as a composite number. (D)</p> Signup and view all the answers

Why is the number 12 not a prime number?

<p>It has more than two factors. (B)</p> Signup and view all the answers

Which of the following pairs of numbers are both prime?

<p>23 and 29 (D)</p> Signup and view all the answers

If listing prime numbers less than 50, after identifying 2, 3, 5, 7, 11, 13, 17, 19, what would be the next prime number you would identify?

<p>23 (D)</p> Signup and view all the answers

A student is asked to list all prime numbers between 30 and 40. Which list is correct?

<p>31, 37 (B)</p> Signup and view all the answers

When using the method described to identify prime numbers, why do we not need to check for multiples of numbers larger than 10 after listing numbers from 1 to 100?

<p>All non-prime numbers will already have been marked. (B)</p> Signup and view all the answers

Which of the following numbers is NOT a prime number?

<p>51 (B)</p> Signup and view all the answers

Which of the following lists contains only prime numbers?

<p>37, 41, 43 (D)</p> Signup and view all the answers

Why is the number 1 considered neither prime nor composite?

<p>It only has one factor. (D)</p> Signup and view all the answers

Which step in identifying prime numbers between 101 and 120 involves eliminating multiples of 5?

<p>Step 4 (B)</p> Signup and view all the answers

If you are listing prime numbers and have eliminated all multiples of 2, 3, and 5, what is the next number you should check for divisibility?

<p>7 (A)</p> Signup and view all the answers

Which of the following best explains why 91 is not a prime number?

<p>It is divisible by 7 and 13. (D)</p> Signup and view all the answers

Which of the following methods is most effective for identifying all prime numbers within a specific range, such as between 101 and 120?

<p>Checking divisibility by prime numbers less than the square root of the upper limit. (A)</p> Signup and view all the answers

What is the purpose of marking numbers divisible by 2, 3, 5, and 7 when finding prime numbers within a range?

<p>To identify composite numbers. (C)</p> Signup and view all the answers

Consider the number 119. It is not divisible by 2, 3, or 5. If using the method described, what is the next step to determine if it's prime?

<p>Divide by 7. (B)</p> Signup and view all the answers

Which of the following statements is correct regarding the distribution of prime numbers?

<p>Prime numbers become less frequent as numbers increase. (B)</p> Signup and view all the answers

Which of the following numbers is NOT a counting number?

<p>0 (C)</p> Signup and view all the answers

What is the key difference between counting numbers and whole numbers?

<p>Whole numbers include 0, while counting numbers do not. (B)</p> Signup and view all the answers

How can you identify an even number?

<p>It is divisible by 2, leaving no remainder. (B)</p> Signup and view all the answers

Which of the following lists contains only counting numbers?

<p>1, 3, 5, 7, 9 (B)</p> Signup and view all the answers

A student is asked to list the first 5 whole numbers. Which of the following answers is correct?

<p>0, 1, 2, 3, 4 (D)</p> Signup and view all the answers

Which of these situations primarily involves using counting numbers?

<p>Tallying the number of students in a classroom. (D)</p> Signup and view all the answers

A number can be divided by two with no remainder. Which of the following statements must be true?

<p>It is an even number. (C)</p> Signup and view all the answers

Which of the following numbers does NOT fit the criteria of having only two factors?

<p>9 (B)</p> Signup and view all the answers

What is the significance of the Greatest Common Factor (GCF) in relation to two or more numbers?

<p>It is the largest number that divides all the numbers without a remainder. (C)</p> Signup and view all the answers

What are the common factors of 18 and 24?

<p>1, 2, 3, 6 (C)</p> Signup and view all the answers

To find the GCF of two numbers using prime factors, what is the initial key step?

<p>Listing all the factors of both numbers. (C)</p> Signup and view all the answers

If two numbers share only one common factor, what must that factor be?

<p>One (D)</p> Signup and view all the answers

Why is the number 1 excluded from being a prime number?

<p>It has only one factor, itself. (C)</p> Signup and view all the answers

Which of the following numbers has exactly three factors?

<p>4 (D)</p> Signup and view all the answers

Which of the following steps is essential when using the sieve method to identify prime numbers?

<p>Listing numbers and marking multiples of primes. (C)</p> Signup and view all the answers

After encircling 5 in the prime number identification process, what is the next step?

<p>Encircle 7 and mark multiples of 7. (D)</p> Signup and view all the answers

What is the highest number of factors for any single number within the range of 1 to 10?

<p>4 (A)</p> Signup and view all the answers

What criterion is used to finalize the list of prime numbers in the sieve method after sieving?

<p>All encircled numbers and unmarked numbers (excluding 1) are prime. (B)</p> Signup and view all the answers

How many numbers in the range of 1 to 15 have only two factors?

<p>6 (B)</p> Signup and view all the answers

A student mistakenly believes that 9 is a prime number. What characteristic of prime numbers does this student misunderstand?

<p>Prime numbers have exactly two distinct factors. (D)</p> Signup and view all the answers

How many prime numbers are there between 1 and 100, according to the method described?

<p>25 (D)</p> Signup and view all the answers

Which of the following sets of numbers consists only of prime numbers?

<p>2, 3, 5, 7, 11 (A)</p> Signup and view all the answers

Which number between 1 and 15 has the most factors?

<p>12 (C)</p> Signup and view all the answers

What do all prime numbers have in common regarding their factors?

<p>They have exactly two factors. (C)</p> Signup and view all the answers

What is the largest prime number that is less than 20?

<p>19 (D)</p> Signup and view all the answers

Identify the number that is a factor of both 12 and 15.

<p>3 (A)</p> Signup and view all the answers

Which of the following pairs of numbers are both factors of 8?

<p>2 and 4 (A)</p> Signup and view all the answers

Why are multiples of prime numbers marked with an 'x' during the prime number identification process?

<p>To exclude composite numbers. (A)</p> Signup and view all the answers

If a number has factors of 1, 2, 3, and 6, what is the number?

<p>6 (C)</p> Signup and view all the answers

Of the numbers listed, which one has factors that include both an even and an odd number greater than 1?

<p>6 (B)</p> Signup and view all the answers

What is the result of expressing 36 as a product of its prime factors?

<p>$2 \times 2 \times 3 \times 3$ (B)</p> Signup and view all the answers

Which of the following is NOT a factor of 36?

<p>8 (A)</p> Signup and view all the answers

From the factors of 36, how many are divisible by 2?

<p>6 (D)</p> Signup and view all the answers

If you divide 36 by all its factors, which factor will give the smallest quotient?

<p>36 (D)</p> Signup and view all the answers

What do you call numbers that when multiplied together give you 45?

<p>Factors (D)</p> Signup and view all the answers

Which list contains all the factors of 20?

<p>1, 2, 4, 5, 10, 20 (C)</p> Signup and view all the answers

A student claims that 4, 5, 9 and 10 are all factors of 45. Is their claim correct?

<p>The student is partially correct; only 5 and 9 are factors of 45. (C)</p> Signup and view all the answers

Identify all the PRIME factors of 45 from the options below:

<p>3 and 5 (D)</p> Signup and view all the answers

If a number has only two factors, 1 and the number itself, what type of number is it?

<p>Prime number (D)</p> Signup and view all the answers

A rectangle has an area of 36 square units. If the length and width are whole numbers, how many different whole number dimensions (length and width) are possible, considering that the order does not matter (i.e., 4x9 is the same as 9x4)?

<p>5 (A)</p> Signup and view all the answers

The number 1 is considered a prime number.

<p>False (B)</p> Signup and view all the answers

A factor of a number divides that number with a remainder.

<p>False (B)</p> Signup and view all the answers

All odd numbers are prime numbers.

<p>False (B)</p> Signup and view all the answers

2 is the smallest prime number.

<p>True (A)</p> Signup and view all the answers

15 is a prime number.

<p>False (B)</p> Signup and view all the answers

The factors of 6 are 1, 2, 3, and 6.

<p>True (A)</p> Signup and view all the answers

A prime number can be divided evenly by more than two numbers.

<p>False (B)</p> Signup and view all the answers

36 divided by 1 equals 36.

<p>True (A)</p> Signup and view all the answers

1, 2, 3, 5 and 6, are all factors of 36.

<p>False (B)</p> Signup and view all the answers

2, 4, 6, 12, 18 and 36 are factors of 36 and are divisible by 2.

<p>True (A)</p> Signup and view all the answers

A number can only be written as a product of two factors.

<p>False (B)</p> Signup and view all the answers

36 can be expressed as a product of prime numbers as: $36 = 2 \times 2 \times 3 \times 3$.

<p>True (A)</p> Signup and view all the answers

The factors of 45 are 1, 3, 5, 9, 15, and 45.

<p>True (A)</p> Signup and view all the answers

7 is a factor of 20.

<p>False (B)</p> Signup and view all the answers

The only factors of 5 are 1 and 5.

<p>True (A)</p> Signup and view all the answers

The factors of 16 are 1, 2, 4, 6, 8, and 16.

<p>False (B)</p> Signup and view all the answers

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

<p>True (A)</p> Signup and view all the answers

The factors of 49 are 1, 7, and 49.

<p>True (A)</p> Signup and view all the answers

The factors of 81 are 1, 3, 9, 27, and 81.

<p>True (A)</p> Signup and view all the answers

In the prime factorization of 40, the missing factor in $40 = 2 \times 4 \times 5$ is 8.

<p>False (B)</p> Signup and view all the answers

In the prime factorization of 72, the missing factor in $72 = 1 \times 2 \times 3 \times 4$ is 4.

<p>True (A)</p> Signup and view all the answers

Prime numbers cannot be identified using tree diagrams.

<p>False (B)</p> Signup and view all the answers

The greatest common factor (GCF) can be found using prime factors.

<p>True (A)</p> Signup and view all the answers

A prime number has only two factors: 1 and itself.

<p>True (A)</p> Signup and view all the answers

A tree diagram can be used to find the GCF of two numbers.

<p>True (A)</p> Signup and view all the answers

The GCF of 11 and 42 is 2.

<p>False (B)</p> Signup and view all the answers

A multiple of a number is the result of dividing that number by another counting number.

<p>False (B)</p> Signup and view all the answers

The first five multiples of 2 are: 2, 4, 6, 8, and 10.

<p>True (A)</p> Signup and view all the answers

Prime numbers have exactly two distinct factors: 1 and themselves.

<p>True (A)</p> Signup and view all the answers

Expressing a number as a product of prime numbers is called prime factorization.

<p>True (A)</p> Signup and view all the answers

The prime factorization of 18 is 2 × 3 × 5.

<p>False (B)</p> Signup and view all the answers

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

<p>True (A)</p> Signup and view all the answers

To find the GCF using prime factors, you multiply all common prime factors.

<p>True (A)</p> Signup and view all the answers

Listing factors is an acceptable method for finding the GCF of two numbers.

<p>True (A)</p> Signup and view all the answers

Two numbers that have no common factors other than 1 are called relatively prime or co-prime.

<p>True (A)</p> Signup and view all the answers

The common factors of 3 and 7 are 1 and 3.

<p>False (B)</p> Signup and view all the answers

All numbers ending in 2, 4, 6, or 8 are even, regardless of their other digits.

<p>False (B)</p> Signup and view all the answers

The number 571 fits into the following even number pattern: 574, 572, 570, ...

<p>False (B)</p> Signup and view all the answers

When counting from 1 to 12, there are exactly 5 even numbers.

<p>False (B)</p> Signup and view all the answers

Even numbers can always be divided into groups of two with no remainder.

<p>True (A)</p> Signup and view all the answers

There are only five even numbers between 81 and 99.

<p>False (B)</p> Signup and view all the answers

The sum of two even numbers is always an odd number.

<p>False (B)</p> Signup and view all the answers

The inverse of an even number is likewise an even number.

<p>False (B)</p> Signup and view all the answers

The numbers 52, 56, and 60 are all even numbers.

<p>True (A)</p> Signup and view all the answers

Among the numbers 71, 78, 82, 83, and 87, only 78 is an even number.

<p>False (B)</p> Signup and view all the answers

The complete sequence of missing even numbers in the pattern 22, 24, 26, _____, _____, _____ is 28, 30, 34.

<p>False (B)</p> Signup and view all the answers

There exist 8 even numbers between 45 and 63.

<p>True (A)</p> Signup and view all the answers

The even numbers between 73 and 93 that are divisible by 4 are 74, 76, 80, 84, 88, 92.

<p>False (B)</p> Signup and view all the answers

The missing even numbers in the pattern 30, __, 34, 36, __, __, 42, __, 46 are 31, 38, 40, 44.

<p>False (B)</p> Signup and view all the answers

Odd numbers are whole numbers that can be divided exactly by 2.

<p>False (B)</p> Signup and view all the answers

When counting from 1 to 12, the numbers 1, 3, 5, 7, 9, and 11 are classified as odd numbers because they each leave a remainder of 1 when divided by 2.

<p>True (A)</p> Signup and view all the answers

The number 2 is an odd number because when you represent it with counters, you have one group of two with no remainder.

<p>False (B)</p> Signup and view all the answers

The GCF of 11 and 42, found using prime factors, is 1.

<p>True (A)</p> Signup and view all the answers

The greatest common factor (GCF) of 30 and 90 is 90, indicating that 30 is not a factor of 90.

<p>False (B)</p> Signup and view all the answers

When finding the GCF of two numbers using the tree diagram method, the branches of the tree must always extend until only composite numbers remain.

<p>False (B)</p> Signup and view all the answers

When determining the GCF of 24 and 156 using common prime factors, one would not include 5 as a potential common prime factor.

<p>True (A)</p> Signup and view all the answers

If a limit is not specified, the list of multiples for any given number will terminate at the tenth multiple.

<p>False (B)</p> Signup and view all the answers

The number 5 is a factor of 36.

<p>False (B)</p> Signup and view all the answers

The factors of 45 include 1, 3, 5, 9, 15, and 45.

<p>True (A)</p> Signup and view all the answers

When expressing 36 as a product of prime numbers, the result is $2 \times 2 \times 3 \times 3$.

<p>True (A)</p> Signup and view all the answers

All factors of 36 are divisible by 2.

<p>False (B)</p> Signup and view all the answers

The number 20 has exactly 4 factors.

<p>False (B)</p> Signup and view all the answers

If a number is divisible by both 2 and 3, it must be a factor of 36.

<p>False (B)</p> Signup and view all the answers

If we divide 36 by each of its factors, the result will always be a whole number.

<p>True (A)</p> Signup and view all the answers

A prime number must have exactly two distinct positive divisors: 1 and itself.

<p>True (A)</p> Signup and view all the answers

The number 1 is considered a primary number because it is only divisible by itself.

<p>False (B)</p> Signup and view all the answers

When identifying prime numbers up to 100 using the sieve method, after encircling 2, you mark all numbers divisible by 4 with an 'x'.

<p>False (B)</p> Signup and view all the answers

After sieving, all numbers that have not been marked with 'x' are composite numbers

<p>False (B)</p> Signup and view all the answers

When finding prime numbers less than 30, 29 is included because it is only divisible by 1 and itself.

<p>True (A)</p> Signup and view all the answers

The largest prime number less than 50 is 49.

<p>False (B)</p> Signup and view all the answers

All prime numbers are odd.

<p>False (B)</p> Signup and view all the answers

After encircling 3 during the sieve process, you proceed to mark all multiples of 9 with 'x'.

<p>False (B)</p> Signup and view all the answers

There are exactly 26 prime numbers between 1 and 100.

<p>False (B)</p> Signup and view all the answers

The numbers 51, 53, and 59 are all consecutive primes.

<p>False (B)</p> Signup and view all the answers

Flashcards

Division

A mathematical process that involves distributing a quantity into equal parts.

Divisor

The number by which another number is divided.

Quotient

The result obtained after performing division.

Remainder

The amount left over when one number does not exactly divide another.

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Division Application

Distributing items into a specific number of groups.

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Budgeting

Planning how to spend money wisely.

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Division in Decision Making

Making choices about resources or expenses.

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What is a dividend?

The number being divided in a division problem.

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What is a divisor?

The number that divides the dividend.

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What is a quotient?

The result of the division.

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What is the Remainder?

The amount left over after division.

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First Step in Division?

Starting from the left, find how many times the divisor "fits" into the dividend.

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Where to Write the Quotient

Write the quotient above the last digit of the dividend you used.

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Next Step After Dividing

Multiply the divisor by the quotient you just wrote down.

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What to do after multiplying?

Subtract the product from the corresponding part of the dividend.

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Bringing Down Numbers

Bring down the next digit of the dividend to continue dividing.

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What is division?

The process of finding out how many times one number contains another.

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What is long division?

A method for dividing numbers, often used for larger numbers.

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What is multiplication in division?

Multiplying the divisor (7) by a number (696).

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What is subtraction in division?

Finding the difference between two amounts.

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What does a zero remainder mean?

After multiplying and subtracting, the remainder should be zero.

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What is checking your answer?

Verifying the division to see if the quotient obtained is correct via multiplication.

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What is the role of the divisor?

Used to divide the dividend to give the answer.

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Short Division

A method of division where the divisor is a single-digit number.

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Long Division

A method of division used when the divisor is multi-digit, involving several steps to find the quotient.

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Dividend

The number being divided in a division problem.

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Division with Remainder

Occurs in division when the dividend is not an exact multiple of the divisor; it's the amount left over.

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Division direction

In short division, start dividing the dividend from left to right.

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Quotient Placement

When dividing, place the result (quotient) above the corresponding digit of the dividend.

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Uneven Division

When dividing, if a digit cannot be divided evenly, consider the next digit.

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8 ten thousands / 2

Ten thousands divided by 2 gives 4 ten thousands.

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Result Placement

Write the result below the corresponding place value.

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Iterative Division

Keep placing results until all the numbers are divided.

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How to check division?

Multiply the divisor by the quotient and subtract the product. Check if the remainder is zero.

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What is a multi-digit divisor?

A multi-digit number requiring a step-by-step method for dividing.

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What is the dividend?

The number you are dividing into (the bigger number).

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What is the divisor?

The number that divides the dividend.

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What is the quotient?

The result you get after dividing.

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Division: Bringing Down

Bring down the next digit of the dividend.

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What is remainder?

The amount left over when the divisor doesn't divide the dividend evenly.

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Short Division Method

A division method where the dividend, divisor, and quotient are arranged in a specific format for simpler calculation.

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Starting Point in Division

Begin the division process by looking at the leftmost digit.

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First Division Step

Determine how many times the divisor 'fits' into the leftmost digit (or digits if the divisor is larger).

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Placing the Quotient

Write the result of each division step (the quotient) above the corresponding digit of the dividend.

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Writing Results

When dividing, write this below the digit in the dividend you're using.

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First Step: Divide Left

The first step is to divide the leftmost digit(s) of the dividend by the divisor.

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What after multiplying?

Subtract the product from the dividend.

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Equal Division

Distributing items equally among a group.

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Individual Share

The number of items each person or group receives.

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Division Remainder

The amount left over after dividing a quantity into equal parts.

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Word Problem

A problem presented in sentence form requiring a mathematical solution.

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Long Division Method

To accurately perform long division requires a step-by-step approach.

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What is Subtraction?

The number from which another number is subtracted

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What is Checking?

Verifying if solution is correct.

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Division: Multiply then Subtract.

Multiply then subtract and then bring down the next number.

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What is short division?

A division method where the dividend, divisor, and quotient are arranged for calculation.

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First step in short division?

Start by dividing the leftmost digit of the dividend by the divisor

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What to do after dividing?

After dividing, multiply the divisor by this most recent result.

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Next step after multiplying?

Subtract the result of multiplication from the corresponding part of the dividend.

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After Dividing...?

Multiply divisor by the last quotient.

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Division Word Problem

A problem presented in a real-world context requiring division to solve.

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Total Quantity

The total number of items being shared or divided.

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Number of Groups

The number of groups or individuals receiving a share.

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Individual Share (Division)

The amount each group or individual receives when dividing equally.

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Division Remainder (Word Problems)

The quantity remaining after dividing a number as evenly as possible.

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57 divided by 12

The remainder when 57 is divided by 12.

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93 divided by 12

The remainder when 93 is divided by 12

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573 divided by 12 result

The answer when 573 is divided by 12, with any remainder.

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Carry out division

Divide the numbers completely.

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Repeated Subtraction

Repeated subtraction is a method to solve division problems by repeatedly subtracting the divisor from the dividend.

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Long division setup

Arrangement of the dividend, divisor, and quotient.

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Divisor Dividend

An example of long division arrangement

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Long division first step

The first step is: Divide

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Long division Multiplication

After dividing, multiply the divisor by number you just wrote down.

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Subtraction in division

Find the difference between two numbers.

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Short Division Arrangement

Arrange dividend, divisor, quotient in specific way.

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Short Division: Start Where?

Starting from the left, divide each digit.

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Short Division: Write Where?

Write the result above the digit you divided.

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Short Division: Can't divide?

If a digit can't be divided, move to the next.

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First Step:

Divide ten thousands by divisor.

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Placing the Result

Write the result under the ten thousands place.

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Iterate Through Places

Repeat process for thousands, hundreds, etc.

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Estimating quotients

Estimating a quotient before performing division.

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Quotient Position

The digit placed above the dividend to show division result.

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Bringing Down Digits

Moving digits to the right in a division problem.

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Checking the Answer

Finding how many times one number contains another.

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What is product?

The product of divisor and quotient

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Estimates vs Exact

Comparison of estimated answers versus exact answers.

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Is quotient an integer?

Ensures that the numbers are divisible.

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What is a whole number?

The digit in front of the decimal indicates a whole number

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Equal groups

Books arranged into groups.

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Finding items per group

Divide total items by number of groups to find items per group.

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Long division: direction

Divide left to right, one digit at a time.

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Where does the quotient go?

Write it above the dividend.

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Next step: Multiplication

Multiply the divisor by the quotient you just wrote.

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What is after multiplying?

Subtract the result from the matching part of dividend.

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What to do after Subtracting?

Bring down the next digit and repeat the division process.

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What is the division direction?

In short division, divide each digit of the dividend by the divisor, working from left to right.

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What is Uneven Division?

If a digit is not evenly divisible by the divisor, combine the remainder with the next digit.

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What is the process of subtraction?

After dividing and subtracting, the result will be the remainder.

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Division: Verification

Multiply the divisor by the quotient to check your work.

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Division: Subtraction

Subtract the product from the dividend to see what remains.

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Long Division: Bring Down

Bring down the next digit to continue the long division process.

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Long Division: Quotient Place

Write it above the dividend in long division process.

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Divide from Left

Start at left side of dividend, moving right.

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Division Process

Solve the division problem systematically.

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Multiplication and verification

Verification uses multiplication

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Estimating Division

Determining how many times one number is contained within another.

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Division: What is Remainder?

The amount remaining after division.

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Division: Subtraction Step

Subtract the product of the divisor and quotient of the dividend.

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Shifting Digits in Division

In long division, shifting to the next digit involves bringing down the next number from the dividend.

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Quotient Meaning

The number of times the divisor goes into the dividend.

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Multiplying in Division

Multiply the divisor (696) by the quotient (8) to estimate the near dividend amount.

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Bringing Down (Division)

Bringing down digit is taking the number and adding to right of reaminder. (7 brought down to 48)

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Zero in Quotient

If a division is impossible write 0 in the quotient (487 / 696)

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Multiplying by Zero

Multiplying by zero results in zero.(696 * 0 = 0)

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Division Algorithm

A method to find a quotient by following simple steps.

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Roman Numerals: I, X, C

Basic symbols used to represent numbers in the Roman numeral system.

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Roman Numeral Subtraction

When a smaller Roman numeral is to the left of a larger one, subtract its value.

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Roman Numeral Addition

When a smaller Roman numeral is to the right of a larger one, add its value

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Roman Numeral Left Repeat Rule

A Roman numeral can not be repeated when written to the left of a greater number.

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Roman Numeral Repeat Limit

Cannot be repeated more than three times when writing to the right of a number.

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Roman Numeral: L

L represents fifty.

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Roman Numeral: C

C represents one hundred.

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Roman Numeral IV

Represents 4 in Roman numerals.

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Roman Numeral IX

Represents 9 in Roman numerals.

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XCIX Value

XCIX can be broken down as (100 - 10) + 9 = 99.

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LIV Value

LIV is equal to 50 + 4 = 54.

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LV Translation

Represents the number 55.

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LIX Translation

Represents the number 59.

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LXXXIX Translation

Represents the number 89.

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LXXII Translation

Represents the Number 72

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CCCXXX

330 in Roman numerals.

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CCXIX

219 in Roman numerals.

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CCXCII

292 in Roman numerals.

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CLXIX

169 in Roman numerals.

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CDXLVII

447 in Roman numerals.

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52 in Roman Numerals

52 in Roman numerals is LII.

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66 in Roman Numerals

66 in Roman numerals is LXVI.

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70 in Roman Numerals

70 in Roman numerals is LXX.

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81 in Roman Numerals

81 in Roman numerals is LXXXI.

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93 in Roman Numerals

93 in Roman numerals is XCIII.

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51 in Roman Numerals

Fifty-one in Roman numerals is LI.

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63 in Roman Numerals

Sixty-three in Roman numerals is LXIII.

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75 in Roman Numerals

Seventy-five in Roman numerals is LXXV.

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84 in Roman Numerals

Eighty-four in Roman numerals is LXXXIV.

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92 in Roman Numerals

Ninety-two in Roman numerals is XCII.

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What is CXVII?

CXVII is 100 + 10 + 5 + 2

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CXVII in words?

CXVII represents one hundred and seventeen.

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What is CDXLVI?

CDXLVI is (500-100) + (50-10) + 6

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CDXLVI in words?

CDXLVI represents four hundred and forty-six.

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What is CIV?

CIV represents one hundred and four.

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What is CXIX?

CXIX represents one hundred and nineteen.

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What is CLXXVI?

CLXXVI represents one hundred and seventy-six

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What is CCXXII?

CCXXII represents two hundred and twenty-two

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What is CCCXLIII?

CCCXLIII equals to Three hundred and forty-three

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What is CDXVII?

CDXVII represents four hundred seventeen.

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Roman Numerals

Symbols representing numbers, used in ancient Rome.

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Arabic Numerals

Numerical system using 1, 2, 3, etc., which is commonly used.

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Roman Numeral for 1

I

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Roman Numeral for 5

V.

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X

Represents ten.

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L

Represents fifty.

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Uses of Roman Numerals

Shows hours on clocks, lists, and rankings.

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Subtraction Rule

Write smaller value to the left of a larger value to subtract.

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Addition Rule

Write smaller values to the right of a larger value to add.

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No Repeat Left

I, X, and C cannot be repeated to the left of a greater number.

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Repeat Thrice Right

I, X, and C can be repeated up to three times when adding.

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CMXC in words

CMXC is nine hundred ninety.

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DCCL in words

DCCL is seven hundred fifty.

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CCCXIV in words

CCCXIV is three hundred fourteen.

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XCI in words

XCI is ninety-one.

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Roman Numeral Addition Rule

IV (4) and IX (9) are ones and added if written to the right of a larger numeral.

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Reading Roman Numerals

Breaking down Roman numerals into their values to read them.

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LV Numeral

55

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LIX Numeral

59

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LXXXIX Numeral

89

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LXXII Numeral

72

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XCV Numeral

95

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Analogue Clock

A clock that shows time using hands and a circular face, often with Roman numerals.

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No Repetition (Left)

I, X, and C cannot be repeated when written to the left of a greater number.

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Max 3 Repeats (Right)

I, X, and C cannot be repeated more than three times when written to the right of a greater number.

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LXV Conversion

65 is written as LXV in Roman numerals. (50 + 10 + 5)

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What is DCCLXXIV?

774 in Roman numerals.

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What is DCLXXIV?

674 in Roman numerals.

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Roman Numeral Conversion

Knowing the value of each number in Roman numerals helps convert to numbers.

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CXVII in Numbers

CXVII represents the number 117. It's a combination of C (100), X (10), V (5), and II (2).

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CDXLVI in Numbers

CDXLVI represents the number 446. It uses CD (500-100 = 400), XL (50-10 = 40), and VI (6).

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CIV in Numbers

CIV represents the number 104. It combines C (100) and IV (4).

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CXIX in Numbers

CXIX represents the number 119. It combines C (100), X (10), and IX (9).

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CLXXVI in Numbers

CLXXVI represents 176. It's a combination of C (100) + L (50) + XX (20) + VI (6).

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CCXXII in numbers

CCXXII represents the number 222. It's two hundreds, two tens, and two ones.

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CCCXLIII in numbers

CCCXLIII represents the number 343. It uses CCC (300), XL (40) and III (3).

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CCXXV in Numbers

CCXXV represents the number 225. It's two hundreds, two tens, and a five.

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CCCXXXVIII in numbers

CCCXXXVIII represents 338. It has 3 hundreds, 3 tens, and an eight.

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CDXVII in number

CDXVII represents the number 417. CD means four hundred, X is ten, and VII is seven.

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What is XCIII?

93 in Roman numerals

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What is LXXXIV?

84 in Roman numerals

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Roman Numbers

Symbols representing numbers, used by ancient Romans.

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Basic Roman Numerals

I, V, X, L, C, D, and M representing 1, 5, 10, 50, 100, 500, and 1000 respectively

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What is 49 in Roman numerals?

XLIX

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Roman Numeral System

Symbols used to represent numbers in a non-decimal system originating in ancient Rome

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CXVII meaning

100 + 10 + 5 + 2 = 117

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CDXLVI meaning

(500 – 100) + (50 – 10) + 6 = 446

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CIV in numerals

One hundred and four is equal to 104

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CXIX in numerals

One hundred and nineteen is the same as number 119

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CLXXVI in numerals

One hundred and seventy-six equals 176

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CCXXII in numerals

Two hundred and twenty-two equals 222

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CCCXLIII in numerals

Number 343 is the same as Three hundred and forty-three

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CCXXV in numerals

Two hundred and twenty-five equals 225

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CCCXXXVIII in numerals

Three hundred and thirty-eight equals 338

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CDXVII in numerals

Four hundred and seventeen equals 417

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What is D?

500 in Roman numerals

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What is D?

Represents 500 in numerals.

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What is M?

Represents 1000 in numerals.

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What does DXI mean?

511 in Roman numerals.

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What does DCLXXIV mean?

674 in Roman numerals.

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What does CMLXXXIV mean?

984 in Roman numerals.

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What is an Even Number?

A whole number that is divisible by 2 with no remainder.

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Last Digit of Even Number

The numbers 0, 2, 4, 6, and 8.

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What are counting numbers?

Numbers you get when you count by ones.

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Grouping by Two's

A method to group items into pairs to identify even numbers.

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Is zero an even number?

An even number.

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What is Listing?

To list items in a specific order.

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What is a number sequence?

Numbers that create a continuous, recognizable pattern.

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Even Numbers

Whole numbers divisible by 2, leaving no remainder.

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Odd Numbers

Whole numbers that are NOT divisible by 2.

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Number Pattern

A sequence of numbers following a specific rule.

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Counting Numbers

Listing numbers in order.

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Even Number Pairs

Numbers with an exact number of pairs.

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Odd Number Remainder

When divided by 2, there's a remainder of 1.

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What are Odd Numbers?

All whole numbers which are not divisible by 2

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Even Numbers in the set 43, 52, 56, 59, 60.

The numbers 56 and 60 are even numbers.

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Missing Even Numbers in the Following Pattern: 22, 24, 26, _____, _____, _____

22, 24, 26, 28, 30, 32

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Lowest Common Multiple (LCM)

The smallest number that is a multiple of two or more numbers.

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Prime Factor Divisors Method

A method to find the LCM by dividing numbers by their prime factors.

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Prime Factor

A factor that is a prime number, can only be divided by 1 and itself.

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LCM Calculation Process

Dividing numbers by common prime factors until you reach 1.

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LCM Result

Product of all prime factors used in the division process to get from all numbers involved to one.

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Prime Number

A number that has only two distinct factors: 1 and itself.

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Why 1 isn't prime?

A number with only one factor (itself), and is therefore not considered prime.

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Step 1: List Numbers

Listing all numbers from 1 to the desired limit.

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Marking Multiples

To mark off numbers divisible by a certain number (other than 1 and itself).

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Encircled/Unmarked Numbers

Numbers that should be written down at the end because they were not crossed out.

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Prime numbers to 100

The numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,61, 67, 71, 73, 79, 83, 89 and 97.

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Primes less than 20

2, 3, 5, 7, 11, 13, 17 and 19.

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Prime Number Identification

Start with listing numbers, then eliminate multiples of each prime.

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First Prime: 2

Encircle the first prime number, 2, and eliminate all multiples of 2.

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Second Prime: 3

After 2, encircle 3, and eliminate all multiples of 3 that aren't already marked.

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Prime Number Definition

A number that has exactly two distinct divisors: 1 and itself.

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Sieve Method

A method to identify prime numbers by eliminating multiples of composite numbers.

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Composite number

A number greater than 1 that is not prime; it has divisors other than 1 and itself.

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Finding primes in a range

Listing all numbers in a given range and eliminating non-prime numbers.

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Divisibility to Identify Prime

Divisibility by 2 means a number is even and therefore not prime (except for 2).

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Divisibility by 3

A number divisible by 3 is a composite unless it is 3 itself.

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Divisibility by 5

A number ending in 0 or 5 is divisible by 5 and thus composite (except for 5).

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Divisibility by 7

If a number is divisible by 7, it's a composite (unless it is 7).

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Prime Divisibility Test

Checking divisibility by prime numbers to determine if a given number is prime.

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Identifying Primes

Prime numbers found among a specific set of numbers.

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Natural Numbers

Counting numbers, also referred to as natural numbers, begin with 1 and continue indefinitely.

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Whole Numbers

The set of numbers including zero and all counting numbers.

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Divisible by 2

When divided by 2, there is no remainder.

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Counting Numbers (8-20)

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19

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First Nine Whole Numbers

0, 1, 2, 3, 4, 5, 6, 7, and 8

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Factors

The numbers that divide evenly into a given number.

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Why isn't 1 prime?

One is not a prime number because it has only one factor.

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Sieve of Eratosthenes

A method to identify prime numbers by systematically eliminating multiples of each number.

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Steps to Find Primes

To find all prime numbers smaller than a given number you must list numbers, encircle 2, mark multiples of 2, encircle 3, mark multiples of 3, etc.

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Multiples of 2

Numbers divisible by 2.

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First Prime Numbers

The first few prime numbers are numbers that have only two factors: one and itself.

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Multiples of 11

A number that is the product of some number and 11.

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Greatest Common Factor (GCF)

The largest number that divides two or more numbers without a remainder.

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Common Factors

Numbers that divide evenly into two or more numbers.

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Prime Factorization

Breaking down a number into its prime number multipliers.

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What is a factor?

A number that divides evenly into another number.

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Finding all factors

Listing all the factors of a given number.

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Even Factor

A factor that is divisible by 2.

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Factor Tree

A diagram used to find the prime factors of a number.

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What are Prime Numbers?

Numbers that can only be divided by 1 and themselves.

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Product of Factors

Expressing a number as multiplication of its factors.

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Factors of 36

1, 2, 3, 4, 6, 9, 12, 18, 36.

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Factors of 45

1, 3, 5, 9, 15, and 45.

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Factor Branches

Representing a number by breaking it down into its factors.

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Factors of Six

The factors of 6 are 1, 2, 3, and 6.

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Factors of Seven

The factors of 7 are 1 and 7.

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Factors of Eight

The factors of 8 are 1, 2, 4, and 8.

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Factors of Nine

The factors of 9 are 1, 3, and 9.

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Factors of Ten

The factors of 10 are 1, 2, 5, and 10.

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Factors of Eleven

The factors of 11 are 1 and 11.

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Factors of Twelve

The factors of 12 are 1, 2, 3, 4, 6, and 12.

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What is a Prime Number?

A number divisible only by 1 and itself.

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Even Prime Number

The only even prime number.

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Primes Between 10 & 20

Prime numbers between 10 and 20: 11, 13, 17, 19.

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Factors of 36 that are divisible by 2

List all the numbers that divide into 36 without a remainder and are divisible by 2.

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What is 'False'?

A number that shows a statement is not valid

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What is factoring?

Breaking down a number into its factors.

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What is an even factor?

A number divisible by 2.

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Product of primes

Repeated multiplication of prime numbers.

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Even factors of 36

2, 4, 6, 12, 18 and 36

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Tree Diagram (for Prime Factorization)

A diagram that breaks down a number into its prime factors.

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Multiple

A number you get by multiplying a number by an integer (1, 2, 3, etc.).

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GCF by Prime Factors

Finding the prime factors of numbers to determine their GCF.

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What are factors?

Numbers that divide evenly into another number.

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Missing factor

Numbers multiplied together to get another number.

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Factor tree diagram

A diagram to break down a number into its factors.

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Prime factorization steps

A step-by-step method to find prime factors.

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Prime Factorization Method (GCF)

A method to find the GCF by identifying common prime factors.

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Listing Method (Factors)

Listing all factors of numbers to find common ones.

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Repeated Division (GCF)

A step-by-step method to find the GCF using prime divisors.

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Listing Method

Find the largest factor with the listing method.

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How to identify even numbers?

The last digit is 0, 2, 4, 6, or 8.

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Consecutive Numbers

Numbers that come one after another.

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Decreasing Pattern

To go down in value.

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Increasing Pattern

To go up in value.

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What is a Number Pattern?

A sequence of numbers that follow a specific rule.

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Not Even Numbers

Whole numbers not divisible by 2.

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Even Number Pattern

A sequence of even numbers with a constant difference of 2 between each number.

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Even Numbers Between...

Finding numbers between 45 and 63 that are exactly divisible by 2.

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Even and Divisible by 4

Even numbers between 73 and 93 that are divisible by 4.

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Missing Even Numbers (Pattern)

A sequence of even numbers with a consistent interval.

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Odd Number Identification (Counters)

Identifying odd numbers using visual aids like counters.

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Remainder of 1 (Grouping)

Numbers which have 1 as a remainder after being grouped by two.

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Finding Multiples

Multiplying a number by counting numbers to get a list of its multiples.

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What is a composite number?

A number greater than 1 that is not a prime number.

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How to identify primes?

List numbers. Encircle 2, mark multiples of 2. Encircle 3, mark multiples of 3. Continue for 5, 7, 11, etc. Prime numbers will be those which are encircled or not marked.

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Prime numbers less than 20

2, 3, 5, 7, 11, 13, 17, 19

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What is a counting number?

A counting number is a whole number greater than zero.

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What does divisible mean?

A number is divisible by another number if the remainder is zero after division.

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What is the Sieve method?

Listing numbers and marking off multiples of known prime numbers (2, 3, 5, 7, etc.) to identify remaining primes.

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Examples of composite numbers

4, 6, 8, 9, 10, 12, 14, 15, 16, 18

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Factors of 36 Divisible by 2

Factors of 36 divisible by 2 are 2, 4, 6, 12, 18 and 36.

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Study Notes

Types of Numbers

Counting Numbers

  • Counting commonly begins with 1, then continues with 2, 3, 4, and so on
  • Counting numbers are also known as natural numbers

Whole Numbers

  • It includes 0 in the set of counting numbers,
  • The list of whole numbers begins: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and continues

Even Numbers

  • Whole numbers that are exactly divisible by 2 are called even numbers
  • The remainder will be 0, if an even number is divided by 2
  • The last digit of an even number is either 0, 2, 4, 6, or 8. Zero is an even number

Odd Numbers

  • Whole numbers not divisible by 2
  • After dividing by two it will leave a remainder of 1

Prime Numbers

  • Whole numbers divisible by 1 and the number itself
  • Has exactly two factors: one and itself
  • The number 1 is not a prime number because it has a single factor which is itself

Factors of a Number

  • A factor is any number which divides that number without a remainder

Greatest Common Factor

  • GCF is the largest number which divides two or more numbers without a remainder

Multiples of Numbers

  • If any counting number is multiplied by another counting number, then the result is called a multiple
  • Multiples of a number can be listed although the list has no end unless a limit is given

Lowest Common Multiple

  • The LCM of two or more numbers is the smallest whole number which is a multiple of those numbers

Roman Numerals

  • Roman numerals 1-50 was introduced in Standard Four
  • In Standard Five, Roman numerals L up to M numbers can be read and written, which correspond to the Arabic numbers (numerals) 50 up to 1 000
  • Roman numerals are used to show the hours on some analogue clocks and watches
  • It also lists items and rankings such as I, II, III and so on
  • They are also used name classrooms, class levels, reading time and writing preliminaries

Basic Roman Numerals

  • The basic Roman numbers are I, V, X, L, C, D and M

Subtraction and addition Roman Numerals

  • When written to the left of a larger number, they are subtracted and increased when written to the right of a larger number, they are added.
  • The numbers V, L and D cannot be subtracted from a larger number
  • V, L and D may be subtracted from a larger number

More on Roman numerals

  • The numbers I, X and C may be subtracted from a larger number:
  • I may be subtracted only from V and X as in IV and IX
  • X may be subtracted only from L and C in XL and XC
  • C may be subtracted only from D and M as in CD and CM
  • May be repeated up to three times, as in III, XXX and CCC
  • There is no Roman symbol for number 0

Division

  • Division involves distributing sets of things or a group of things into a specified number of parts
  • In division, the number being divided is the dividend
  • The number which divides the dividend is the divisor
  • The answer in division is the quotient

Division with Remainder : Long division

  • In long division when you cannot divide a number, you bring down the next digit
  • Then the divisor involves multiplying and writing it below the dividend and subtracted to get a number then divide again

Division with Remainder : Short division method

  • The addition of ones to a given number involves summing the ones present in the dividend with the remainder during short division

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Related Documents

Division of Numbers PDF
Roman Numerals (PDF)

Description

Learn how to divide numbers up to one million using long and short division methods, with divisors up to three digits. Understand remainders. Division skills helps in budgeting, expense management, and resource allocation.

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