PS4MA Multiplication Medium

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Questions and Answers

What result do you get when multiplying 62 by 4?

  • 232
  • 240
  • 264
  • 248 (correct)

When multiplying 25 by 6, what is written in the ones place after the first step?

  • 0 (correct)
  • 3
  • 8
  • 5

What is the total when 41 is multiplied by 9?

  • 492
  • 400
  • 369 (correct)
  • 369 (correct)

In the multiplication of 27 by 12, what do you regroup after the first calculation?

<p>10 ones into 1 ten (A)</p> Signup and view all the answers

What is the correct sum of the results after multiplying 23 by 21?

<p>483 (A)</p> Signup and view all the answers

When calculating 38 multiplied by 7, what is its expected result?

<p>276 (A)</p> Signup and view all the answers

In the multiplication process, which of the following does not occur when finding 49 multiplied by 4?

<p>Regrouping hundreds into thousands (B)</p> Signup and view all the answers

What is written in the tens place when multiplying 2 tens by 6 in the problem 25 x 6?

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

What is the first step in multiplying 64 by 2?

<p>Multiply 4 by 2 (B)</p> Signup and view all the answers

What is the result of multiplying 72 by 8?

<p>576 (D)</p> Signup and view all the answers

How is the sum calculated in the multiplication of 217 by 4 after all steps?

<p>28 + 40 + 800 = 868 (A)</p> Signup and view all the answers

What is the product of 3125 and 12?

<p>37,500 (D)</p> Signup and view all the answers

Which method is used to multiply numbers horizontally according to the provided examples?

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

What is the first operation performed when using the box method for 276 x 123?

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

In the example 42538 x 39, what is the result of multiplying 42538 by 3 tens?

<p>1,276,140 (C)</p> Signup and view all the answers

What mistake might a student make when regrouping in the operation 4 x 7 in 217 x 4?

<p>Forgetting to write the result in the ones place (B)</p> Signup and view all the answers

Which of the following calculations contributes to the hundreds place in the calculation of 42538 x 39?

<p>42538 x 3 (A)</p> Signup and view all the answers

Which of the following accurately reflects what occurs after multiplying 42538 by 9 in the example provided?

<p>The sum is calculated directly (A)</p> Signup and view all the answers

What is the total number of bars of soap bought if a businessman purchased 170 boxes, each containing 20 bars?

<p>3,400 bars (A)</p> Signup and view all the answers

If a school bought 5,624 crates of soda with each crate containing 24 bottles, how many bottles did they purchase?

<p>134,976 bottles (D)</p> Signup and view all the answers

How many sacks of beans will a bus carry after making 19 trips if it carries 60 sacks per trip?

<p>1,140 sacks (A)</p> Signup and view all the answers

If an airport serves 462,015 passengers each month, how many passengers will be served in five months?

<p>2,310,075 passengers (C)</p> Signup and view all the answers

What is the result of multiplying 239,586 by 24?

<p>5,454,144 (A)</p> Signup and view all the answers

In how many weeks will a farmer who has 5,998 hens produce a total of 83,964 eggs if each hen lays two eggs per day?

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

What is the product of 4181 multiplied by 54?

<p>225,774 (A)</p> Signup and view all the answers

If a nursery plants 3,841 trees and there are 389 nurseries, how many trees were planted in total?

<p>1,509,289 trees (C)</p> Signup and view all the answers

What do you get when you multiply 872 by 13?

<p>11,336 (A)</p> Signup and view all the answers

What is the total number of books printed by a factory in 317 days if it prints 685,390 books each day?

<p>217,513,030 (C)</p> Signup and view all the answers

Flashcards

Multiplication

Multiplication is a mathematical operation that combines two numbers, called factors, to find their product or total.

One-Digit Multiplier

A one-digit multiplier is a number with only one digit, used in multiplication.

Two-Digit Multiplier

A two-digit multiplier is a number with two digits, used in multiplication.

Place Value Expansion

The process of expanding a number into its place values (ones, tens, hundreds, etc.)

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Regrouping (Carrying)

The process of carrying over extra digits from one place value to the next during multiplication.

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Two-Digit by One-Digit Multiplication

Multiplying two-digit numbers by a one-digit multiplier involves multiplying each digit of the two-digit number by the one-digit multiplier, then adding the results.

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Two-Digit by Two-Digit Multiplication

Multiplying two-digit numbers by a two-digit multiplier involves multiplying each digit of the first number by each digit of the second number, then adding the results.

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Vertical Alignment

A vertical alignment of numbers by place values, used for multiplication.

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Combining (Addition of Partial Products)

The act of combining results from individual multiplications during a complex multiplication problem.

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Decimal Point Shift (Multiplication by 10, 100, etc.)

The concept of multiplication where multiplying by 10, 100, etc., simply moves the decimal point to the right.

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Traditional Multiplication

A method of multiplying numbers by breaking down the process into smaller steps, focusing on individual digits and place values. It involves multiplying each digit of the multiplicand by each digit of the multiplier, then adding the results.

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Multiplication by Boxes

A visual method of multiplication where numbers are placed in boxes, and the multiplication of individual digits is performed to fill the boxes. The results are then added diagonally to get the final product.

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Multiplication of Multi-Digit Numbers by a Single-Digit

The process of multiplying a multi-digit number by a single-digit number, breaking it down into individual digits and place values. Each digit is multiplied separately and then added together.

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Horizontal Arrangement Method

The method of multiplying numbers by writing them in a horizontal format and then multiplying each digit of the multiplier by each digit of the multiplicand, starting from the ones place and moving to the left.

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Regrouping

The concept of carrying over a value from one place value to the next place value when the result of a multiplication exceeds the capacity of that place value. For example, if 7 x 8 = 56, the 5 tens are carried over to the tens place.

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Place Value

The value a digit holds in a number based on its position. For example, in the number 123, the digit 1 represents the hundreds place value.

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Multiplicand

The number being multiplied in a multiplication problem.

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Multiplier

The number that indicates how many times the multiplicand is to be added to itself.

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Product

The result obtained after performing a multiplication operation. It is the product of the multiplicand and the multiplier.

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Multiplication of Multi-Digit Numbers by Two-Digit

The process of multiplying a multi-digit number by a two-digit number, breaking it down into steps and focusing on individual digits and place values.

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Decimal Shift Multiplication

The process of multiplying a number by ten or a power of ten (like 100, 1000) simply shifts the decimal point to the right by the number of zeros in the multiplier.

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Multi-Digit Multiplication

When multiplying numbers with multiple digits (like 123 x 45), the process involves multiplying each digit of the first number by each digit of the second number, then adding the results.

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Carrying in Multiplication

In multi-digit multiplication, we often need to carry digits over to the next place value when the product of two digits exceeds 9.

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Word Problem: Multiplication

A word problem involving multiplication asks you to find the total amount when combining equal groups or quantities.

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Vertical Alignment in Multiplication

When multiplying two-digit numbers, align the numbers vertically by place value (ones, tens). This helps make the multiplication process organized and easier to manage.

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Study Notes

Multiplication of Whole Numbers

  • Multiplication is a mathematical operation used in various contexts, including business, construction, statistics, sports, and finance.

Introduction to Multiplication

  • This chapter explores multiplying whole numbers, a fundamental mathematical concept applied in everyday life.

Multiplication of Two-Digit Numbers by a One-Digit Multiplier

  • Example 1 (62 × 4):

    • Multiply the ones place (2 × 4 = 8).
    • Multiply the tens place (6 × 4 = 24). Write down the 4 in the tens place and regroup the 20 into hundreds.
    • Combine the results (248).
  • Example 2 (25 × 6):

    • Multiply the ones place (5 × 6 = 30). Write down the 0 in the ones place and regroup the 3.
    • Multiply the tens place (2 × 6 = 12). Add the regrouped 3 (12 + 3 = 15). Write down the 5 in the tens place and the 1 in the hundreds place
    • Combine the results (150).

Multiplication of Two-Digit Numbers by a Two-Digit Multiplier

  • Example 1 (23 × 21):

    • Multiply the first number by the ones place of the second number (23 × 1 = 23).
    • Multiply the first number by the tens place of the second number, shifting the result one place to the left (23×20 = 460).
    • Add the two results (23 + 460 = 483).
  • Example 2 (78 × 69):

    • Multiply the ones place (9 × 8 = 72). Write down the 2 and carry over the 7tens.
    • Multiply the tens place (9 × 70 = 630). Add the carried 70 (630 + 70 = 700). Write down the 0 and carry over the 7 hundreds.
    • Multiply the first number by the tens place of the second number, shifting the result one place to the left (70 × 60 = 4200). Add the previous carried 700 (4200 + 700 = 4900). Write down the 0 in the hundreds place and the 9 in the thousands place.
    • Combine the two results (702 + 4680 = 5382).

Multiplication of Three-Digit Numbers by a Two-Digit Multiplier

  • Example 1 (78 × 69):
    • Multiply vertically aligning the digits by place values ( ones, tens and hundreds).
    • Add the results from the previous steps (702 + 4680 = 5382).
    • Writing vertically and multiplying each digit by the ones and tens, carrying over as needed and then adding.

Multiplication of Numbers with up to Six Digits by a Multiplier

  • Example methods are demonstrated including horizontal arrangements and vertical arrangements
  • Examples and exercises are provided for different multiplication scenarios.

Word Problems

  • Several word problems are included for practice applying multiplication to real-world scenarios.
    • Examples include calculating total items, amounts, etc based on specific parameters.

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