352 Questions
What is the result of a + 0?
a
Which of the following properties allows you to regroup numbers when adding or multiplying?
Associative Property
What is the purpose of the summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is the distributive property of multiplication over addition?
a × (b + c) = a × b + a × c
What is the result of a × 1?
a
Which of the following properties is not applicable to subtraction and division?
Commutative Property
What is the benefit of using the commutative and associative properties in calculations?
It simplifies the calculations
What is the purpose of the distributive property?
To break down complex multiplications into simpler parts
What is the purpose of carrying over in multiplication?
To write down the last digit of the product and carry over any extra value to the next column
What is a prime number?
A number that has exactly two distinct positive divisors: 1 and itself
What is the process of expressing a number as the product of its prime factors?
Prime factorization
What is the purpose of finding the least common multiple (LCM) of two or more numbers?
To find a common denominator for adding fractions
What is the formula to find the distance traveled given the speed and time?
Distance = Speed × Time
What is a multiple of a number?
The product of a number and an integer
How do you find the highest common factor (HCF) of two or more numbers?
Take the lowest power of each prime factor that appears in the factorization of each number
What is the purpose of finding the highest common factor (HCF) of two or more numbers?
To simplify fractions to their lowest terms
How do you determine if a number is prime?
By checking whether it can be divided evenly by any prime number smaller than its square root
What is the purpose of calculating rate in a problem?
To find the time required to complete a task
What is the purpose of estimating in calculations?
To make quick decisions and check the reasonableness of results
When estimating products, what is the recommended method of rounding?
Rounding to the nearest thousand
What is the purpose of compensating in calculations?
To adjust for errors introduced by rounding
What is the method of addition where numbers are broken down into parts and added separately?
Expanded Notation
What is the method of subtraction where numbers are aligned by their place values and subtracted column by column?
Column Subtraction
What is the purpose of the borrowing technique in subtraction?
To increase the top digit by 10 while decreasing the digit in the column from which you borrowed by 1
What is the method of multiplication where numbers are broken down into smaller parts and multiplied separately?
Multiplication in Parts
What is the process of breaking down the division into smaller, manageable steps?
Long Division
What is the result of dividing a number by another number and then continuing to divide until you can’t go any further?
The remainder
What is the total error in compensating for rounding errors?
The sum of the errors introduced by rounding each number
What is the result of multiplying a positive integer and a negative integer?
Negative
What is the result of adding a positive integer and its additive inverse?
Zero
What is the symbol used to indicate 'greater than' when comparing integers?
>
What is the result of subtracting a positive integer from another positive integer?
Depends on the integers
What is the cube of a negative integer?
Negative
What is the property of multiplication that states the order of multiplication does not change the product?
Commutative Property
What is the result of dividing a positive integer by a negative integer?
Negative
What is the property of addition that states that integers can be added in any order?
Associative Property
What is the square root of a positive integer?
Both positive and negative
What is the result of adding a negative integer to its additive inverse?
Zero
What is the result of multiplying a positive integer and a negative integer?
Negative
Which property of integers states that changing the order of the numbers does not change the sum?
Commutative Property
What is the additive inverse of an integer?
A number that is subtracted from the integer to get 0
What is the result of multiplying two negative integers?
Positive
What is the purpose of sharing based on work done?
To express the total amount to be shared in the ratio of hours worked
Which property of integers states that changing the grouping of numbers does not change the sum?
Associative Property
How do you calculate the selling price of an article after a discount has been applied?
Subtract the discount amount from the marked price
What is the result of subtracting a larger integer from a smaller one?
Negative
What is the result of multiplying an integer by -1?
The additive inverse of the integer
What is the formula for simple interest?
Interest = Principal × Rate × Time
What is the result of multiplying two negative integers?
A positive integer
What is the absolute value of an integer?
The distance between the number and 0 on the number line
What is the result of dividing two integers with the same sign?
Positive
What is the purpose of scaling quantities in recipes?
To scale up or down the quantities of ingredients as needed
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the purpose of equivalent fractions?
To represent the same value
What happens when you add a positive integer to another positive integer?
The value increases
What is the result of subtracting a negative integer from a positive integer?
A positive integer
How do you calculate the profit percentage of an article?
By finding the difference between the selling price and the cost price, dividing by the cost price, and multiplying by 100
What is the result of dividing a positive integer by a negative integer?
A negative integer
What is the key concept in simplifying fractions?
Dividing both the numerator and the denominator by their greatest common divisor
What is the formula for adding fractions with different denominators?
( \frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d} )
What is the result of multiplying a fraction by its reciprocal?
1
What is the definition of a mixed number?
A combination of a whole number and a fraction
What is the formula for converting a fraction to a percentage?
( \text{Percentage} = \frac{a}{b} \times 100 )
What is the term for fractions that have the same value but different forms?
Equivalent fractions
What is the formula for dividing fractions?
( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} )
What is the key concept in finding a fraction of a fraction?
Multiplying the fractions together
What is the term for the process of converting a fraction to its simplest form?
Simplifying
What is the formula for multiplying fractions?
( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )
What is the formula to find the comparison as a percentage?
(Part ÷ Whole) × 100
When adding decimal fractions, what is the first step?
Align the decimal points
What is the purpose of converting decimal fractions to whole numbers in multiplication?
To eliminate the decimals
When dividing decimal fractions, what is the first step?
Convert the divisor to a whole number
What is the purpose of adjusting the result in multiplication of decimal fractions?
To adjust the decimal place correctly
How do you divide a total amount by a certain number of people?
Convert the total amount to a decimal and divide
What is the purpose of multiplying the volume by the weight per unit volume in weight calculations?
To find the total weight
What is the key concept in adding and subtracting decimal fractions?
Aligning decimal points
What is the purpose of multiplying the weight by the cost per unit weight in cost calculations?
To find the total cost
What is the final step in multiplying decimal fractions?
Adjust the result by dividing by the appropriate power of 10
What is the formula to multiply two fractions?
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
What is the formula to divide a fraction by another fraction?
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
How do you simplify a fraction?
Dividing both the numerator and denominator by their greatest common divisor
What is the formula to convert a fraction to a percentage?
$\frac{a}{b} = \frac{a}{b} \times 100$
What is the formula to find the percentage of a given number?
$\left( \frac{a}{b} \right) \times \text{Number}$
How do you increase a number by a certain percentage?
Add the percentage of the original number to the original number
What is the formula to find the percentage change?
$\left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$
What is the purpose of fractions in real-world applications?
To represent parts of a whole
What is the meaning of a percentage?
A fraction of 100
What is the formula to convert a percentage to a fraction?
$\frac{\text{Percentage}}{100}$
Which property of whole numbers states that the order of factors does not change the product?
Commutative Property of Multiplication
What is the purpose of the associative property of addition?
To regroup numbers when adding or multiplying
What is the result of using the distributive property of multiplication over subtraction?
a × (b - c) = a × b - a × c
Which of the following is a key point of the commutative property of addition?
Changing the order of numbers in addition does not change the result
What is the purpose of using the commutative and associative properties in calculations?
To simplify calculations by changing the order of operations
Which of the following is a property of whole numbers?
a + 0 = a
What is the result of using the associative property of multiplication?
a × (b × c) = (a × b) × c
Which of the following is a benefit of using the distributive property?
It allows us to break down complex multiplications into simpler parts
What is the primary purpose of finding the highest common factor (HCF) of two or more numbers?
To simplify fractions to their lowest terms
What is the process of expressing a composite number as the product of its prime factors called?
Prime factorization
What is the role of carrying over in multiplication?
To write down the last digit of the product
How do you find the least common multiple (LCM) of two or more numbers?
Take the highest power of each prime factor
What is the purpose of calculating rate in a problem?
To compare the time taken by different machines
What is the method of expressing a ratio?
As a fraction in its lowest terms
What is a characteristic of a prime number?
It has exactly two distinct positive divisors: 1 and itself
How do you determine if a number is prime?
By checking if it can be divided evenly by any prime numbers smaller than its square root
What is the purpose of using the formula for distance and time?
To calculate the time taken to travel a certain distance
What is the benefit of using the step-by-step division method?
It allows you to divide numbers step-by-step, starting with the leftmost digits
What is the process of scaling quantities in a recipe?
Multiplying the number of ingredients by the ratio of ingredients to servings
How do you determine which shapes or objects are more similar by comparing their dimensions?
By comparing their ratios
What is the formula for calculating profit percentage?
Profit percentage = (selling price - cost price) / cost price * 100
What is the result of adding a positive integer and a negative integer?
May be positive or negative
What is the purpose of dividing quantities in a ratio?
To find the value of one part
What is the formula for calculating simple interest?
Simple interest = principal * rate * time
How do you increase a quantity in a ratio?
By multiplying the quantity by the factor needed to reach the desired ratio
What is the purpose of comparing ratios in speed comparisons?
To determine which entity is the fastest
What is the result of subtracting a negative integer from a positive integer?
Always positive
What is the purpose of finding the absolute value of an integer?
To find the distance between the number and zero on the number line
What is the purpose of estimating in calculations?
To check the reasonableness of results
When rounding off numbers, what should you do to correct for the error introduced?
Subtract the error from the rounded result
What is the method of addition where numbers are broken down into parts and added separately?
Expanded notation
What is the purpose of the borrowing technique in subtraction?
To make subtraction easier
What is the method of multiplication where numbers are broken down into smaller parts and multiplied separately?
Multiplication in parts
What is the process of breaking down the division into smaller, manageable steps?
Long division
What is the result of dividing a number by another number and then continuing to divide until you can’t go any further?
The remainder
What is the total error in compensating for rounding errors?
The sum of the errors introduced by rounding each number
What is the purpose of column addition?
To simplify addition by aligning numbers by their place values
What is the method of subtraction where numbers are aligned by their place values and subtracted column by column?
Column subtraction
What is the result of the square of a negative integer?
Positive
What is the effect of adding a negative integer to a positive integer?
It decreases the value
What is the result of the cube of a negative integer?
Negative
What is the result of subtracting a positive integer from another positive integer?
Depends on the values of the integers
What is the property of integers that allows you to regroup numbers when adding or subtracting?
Associative Property
What is the result of multiplying two positive integers?
Positive
What is the result of dividing a positive integer by a negative integer?
Negative
What is the additive inverse of an integer?
A negative version of the integer
What is the result of the cube root of a negative integer?
Negative
What is the result of multiplying a positive integer and a negative integer?
Negative
What is the formula to divide a fraction by another fraction?
a/b ÷ c/d = ad/bc
What is the result of multiplying two fractions?
The product of the numerators divided by the product of the denominators
What is the formula to simplify a fraction?
a/b = a ÷ GCD(a, b)/b ÷ GCD(a, b)
What is the formula to convert a fraction to a percentage?
Percentage = a/b × 100
What is the formula to find the percentage of a given number?
Percentage of a number = (Percentage/100) × Number
What is the result of multiplying a fraction by its reciprocal?
1
What is the formula to find the increased value of a number by a percentage?
Increased Value = Original Number + (Percentage/100) × Original Number
What is the purpose of finding the least common multiple (LCM) of the denominators when adding or subtracting fractions?
To find a common denominator
What is the formula to find the percentage change?
Percentage Change = (New Value - Original Value)/Original Value × 100
What is the method to find a fraction of a fraction?
Multiply the fractions together
What is the result of dividing a fraction by a whole number?
A fraction with the same numerator and a new denominator
What is the formula to convert a percentage to a fraction?
Fraction = Percentage/100
What is the formula for converting a fraction to a percentage?
Percentage = (a/b) × 100
What is the result of multiplying two fractions together?
A fraction with the product of the numerators and denominators
What is the result of multiplying a positive integer and a negative integer?
Negative
What is the result of dividing a fraction by 1?
The original fraction
What is the purpose of simplifying a fraction?
To make it easier to work with
Which property of integers states that changing the order of the numbers does not change the product?
Commutative Property
What is the formula for finding the equivalent fraction of a given fraction?
(a/b) = (a×k)/(b×k)
What is the additive inverse of an integer?
Its negative counterpart
What is the result of multiplying two negative integers?
Positive
What is the result of adding a fraction and its reciprocal?
1
What is the formula for subtracting fractions?
(a/b) - (c/d) = (a×d - b×c)/(b×d)
Which property of integers states that changing the grouping of numbers does not change the sum?
Associative Property
What is the result of adding a positive integer and its additive inverse?
Zero
What is the purpose of converting a fraction to a decimal?
To make it easier to work with in calculations
What is the purpose of the distributive property?
To multiply a number by a sum of numbers
What is the absolute value of an integer?
Its distance from zero on the number line
What is the result of subtracting a larger integer from a smaller one?
Negative
Which property of integers states that adding zero to any number does not change the number?
Identity Property
What is the correct formula to express a comparison as a percentage?
(Part / Whole) × 100
When adding or subtracting decimal fractions, what is the first step?
Align the decimal points
What is the purpose of converting decimal fractions to whole numbers when multiplying?
To eliminate the decimals
When dividing a decimal fraction by a whole number, what is the correct step?
Convert the divisor to a whole number by multiplying both numbers by a power of 10
What is the purpose of dividing a total amount by a certain number of people?
To divide the amount equally among the people
What is the correct step in multiplying decimal fractions?
Convert the numbers to whole numbers, multiply, and then adjust the result
What is the purpose of adjusting the result in multiplication of decimal fractions?
To adjust the decimal place to its correct position
When dividing a decimal fraction by another decimal fraction, what is the correct step?
Convert the divisor to a whole number by multiplying both numbers by a power of 10
What is the purpose of converting the divisor to a whole number in division of decimal fractions?
To make the division easier to perform
What is the key point to remember when adding or subtracting decimal fractions?
Align the decimal points
What is the result of applying the commutative property of addition to the equation 5 + 2?
2 + 5
Which of the following expressions demonstrates the associative property of multiplication?
(2 × 3) × 4
What is the result of applying the distributive property to the equation 3 × (4 + 2)?
3 × 4 + 3 × 2
Which of the following statements is true about the additive property of 0?
Adding 0 to a number does not change the result.
What is the result of applying the associative property of addition to the equation (2 + 3) + 4?
2 + (3 + 4)
Which of the following expressions demonstrates the commutative property of multiplication?
3 × 2
What is the result of applying the distributive property to the equation 2 × (5 - 3)?
2 × 5 - 2 × 3
Which of the following statements is true about the multiplicative property of 1?
Multiplying a number by 1 does not change the result.
What is the primary purpose of estimating in calculations?
To make quick decisions and check the reasonableness of results
What is the benefit of using the expanded notation method for addition?
It breaks down numbers into their component parts
What is the purpose of the borrowing technique in subtraction?
To rearrange parts to make subtraction easier
What is the benefit of using the compensation method for rounding errors?
It adjusts for the errors introduced by rounding
What is the purpose of breaking down the multiplication into smaller parts?
To simplify the calculation by breaking it down into smaller, manageable parts
What is the result of not compensating for rounding errors?
The result is less accurate
What is the purpose of using the column addition method?
To align numbers by their place values and add each column
What is the benefit of using the multiplication in parts method?
It breaks down the multiplication into smaller, manageable parts
What is the purpose of rounding numbers to the nearest ten, hundred, or thousand?
To simplify the calculation by making it easier to add or subtract
What is the result of not adjusting for the total error in compensating for rounding errors?
The result is less accurate
What is the result of multiplying a positive integer by the cube of a negative integer?
A negative integer
What is the result of adding a positive integer and the cube root of a negative integer?
A negative integer
Which property of integer operations is used to simplify the expression 2 × (3 + 5)?
Distributive Property of Multiplication
What is the result of subtracting a negative integer from another negative integer?
A positive integer
Which statement is true about the sum of an integer and its additive inverse?
The sum is always zero
What is the result of adding a positive integer and its multiplicative inverse?
1
Which property of integer operations is used to simplify the expression 2 + (3 + 5)?
Associative Property of Addition
What is the result of multiplying a negative integer by the square root of a positive integer?
A negative integer
Which statement is true about the product of two negative integers?
The product is always positive
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the primary purpose of scaling quantities in recipes?
To adjust the quantity of ingredients for a specific number of servings
Which of the following is a characteristic of simple interest?
Interest is calculated on the principal only
When comparing ratios of shapes or objects, what is the primary goal?
To identify which shapes or objects are more similar
What is the result of multiplying a positive integer by a negative integer?
Always negative
What is the primary purpose of dividing quantities in a ratio?
To find the value of each part of the ratio
Which of the following is a characteristic of profit calculation?
Profit is calculated as a percentage of the cost price
What is the primary purpose of calculating the absolute value of an integer?
To determine the distance of the number from zero
Which of the following is a characteristic of compound interest?
Interest is calculated on the principal and any accrued interest
What is the result of adding a positive integer and its additive inverse?
Always zero
What is the primary purpose of calculating the discount amount?
To find the selling price of the article
What is the key concept in finding the prime factorization of a number?
Every composite number can be expressed as a product of its prime factors, and this representation is unique, apart from the order of the factors.
What is the purpose of finding the highest common factor (HCF) of two or more numbers?
To find the largest number that divides two or more numbers without leaving a remainder.
What is the formula to find the distance traveled given the speed and time?
Distance = Speed × Time
What is the key concept in understanding multiples and factors?
Multiples of a number form a sequence where each term is that number multiplied by an integer.
What is the purpose of calculating rate in a problem?
To describe how one quantity changes in relation to another.
What is the key concept in understanding prime numbers?
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
What is the method of dividing a number into smaller, manageable steps?
Step-by-step division
What is the key concept in understanding least common multiple (LCM) of two or more numbers?
The LCM is the largest number that divides two or more numbers without leaving a remainder.
What is the purpose of finding the least common multiple (LCM) of two or more numbers?
To find the common denominator for adding fractions.
What is the method of multiplying a number by breaking it down into smaller parts and multiplying separately?
Partial products
Which property of integers allows us to change the order of integers when adding or multiplying without changing the result?
Commutative Property
What is the result of multiplying two integers with different signs?
Always negative
What is the purpose of the additive inverse of an integer?
To change the sign of an integer
Which property of integers allows us to regroup numbers when adding or multiplying without changing the result?
Associative Property
What is the result of adding a positive integer and its additive inverse?
Always zero
What is the primary purpose of converting decimal fractions to whole numbers in multiplication?
To ensure accurate placement of the decimal point in the result
What is the property of integers that states that multiplying any number by one does not change the value of that number?
Identity Property
What is the result of subtracting a larger integer from a smaller one?
Always negative
When dividing a total amount by a certain number of people, what should be done first?
Convert the total amount to a decimal
What is the purpose of the distributive property of multiplication over addition?
To multiply a number by a sum of numbers
What is the purpose of multiplying both numbers by a power of 10 in division of decimal fractions?
To make the divisor a whole number
What should be done to the result after multiplying decimal fractions?
Divide the result by the power of 10
What is the result of multiplying two negative integers?
Always positive
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the correct order of operations when adding decimal fractions?
Align decimal points, add corresponding digits, place the decimal point
What is the purpose of weight and cost calculations in problem solving?
To calculate the cost per unit weight
When dividing decimal fractions, what should be done to the divisor?
Convert the divisor to a whole number
What is the correct formula for comparison as a percentage?
(Part/Whole) × 100
What is the purpose of adjusting the result after multiplying decimal fractions?
To ensure accurate placement of the decimal point
What should be done to the dividend and divisor in division of decimal fractions?
Multiply both by the same power of 10
What is the result of dividing a fraction by its reciprocal?
1
What is the formula for converting a fraction to a percentage?
Fraction × 100
What is the result of simplifying a fraction where the numerator and denominator have a greatest common divisor (GCD) of 2?
The numerator and denominator are divided by 2
What is the formula for finding the percentage of a given number?
Percentage × Number
What is the result of increasing a number by 25% and then decreasing it by 20%?
The number is decreased by 5%
What is the formula for finding the percentage change between two values?
((New Value - Original Value) ÷ Original Value) × 100
What is the result of multiplying a fraction by its reciprocal?
1
What is the formula for converting a percentage to a fraction?
Percentage ÷ 100
What is the result of dividing a fraction by a fraction?
The quotient of the two fractions
What is the formula for finding a fraction of a fraction?
First Fraction × Second Fraction
What is the result of dividing a fraction by its reciprocal?
1
Which of the following is a correct way to simplify a fraction?
Divide both the numerator and the denominator by their greatest common divisor
What is the result of multiplying a fraction by its reciprocal?
1
How do you convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100
What is the result of adding a fraction to its additive inverse?
0
How do you find the equivalent fraction of a given fraction?
Multiply both the numerator and the denominator by a non-zero integer
What is the result of subtracting a fraction from its additive inverse?
2 times the original fraction
How do you convert a mixed number to an improper fraction?
Multiply the whole number part by the denominator and add the numerator
What is the result of multiplying a fraction by a whole number?
The original fraction multiplied by the whole number
How do you find the fraction of a fraction?
Multiply the fractions together
Which of the following properties is a result of the commutative property of multiplication?
a × b = b × a
Using the associative property of addition, which of the following expressions is equivalent to (a + b) + c?
a + (b + c)
What is the result of applying the distributive property to the expression 2 × (3 + 4)?
2 × 3 + 2 × 4
Which of the following properties can be used to simplify the calculation (a + b) + c + d?
Associative property of addition
What is the result of applying the distributive property of multiplication over subtraction to the expression 2 × (3 - 4)?
2 × 3 - 2 × 4
Using the commutative property of addition, which of the following expressions is equivalent to a + b + c?
c + a + b
Which of the following properties can be used to simplify the calculation a × (b + c)?
Distributive property of multiplication over addition
What is the result of applying the associative property of multiplication to the expression (a × b) × c?
a × (b × c)
What is the main purpose of estimating in calculations?
To get a quick and close approximation
What is the result of rounding 386 to the nearest hundred?
390
What is the method of subtraction where numbers are aligned by their place values and subtracted column by column?
Column Subtraction
What is the purpose of the borrowing technique in subtraction?
To make subtraction easier by borrowing from higher place values
What is the method of multiplication where numbers are broken down into smaller parts and multiplied separately?
Multiplication in Parts
What is the result of multiplying a positive integer and the additive inverse of another positive integer?
A negative integer
What is the total error in compensating for rounding errors?
The sum of the errors introduced by rounding each number
If $a$ and $b$ are positive integers, what is the result of $(a + b) - (a - b)$?
$2b$
What is the purpose of breaking down the division into smaller, manageable steps?
To make the division easier to understand
What is the result of dividing a number by another number and then continuing to divide until you can’t go any further?
A remainder
What is the result of subtracting a negative integer from a positive integer?
A positive integer
If $a$ and $b$ are integers, what is the result of $a × (-b)$?
$-ab$
What is the main purpose of rounding off and compensating in calculations?
To make the calculation easier and faster
What is the result of adding a positive integer and its additive inverse?
Zero
What is the method of addition where numbers are broken down into parts and added separately?
Expanded Notation
If $a$ and $b$ are integers, what is the result of $(-a) + (-b)$?
$-a - b$
What is the result of dividing a negative integer by another negative integer?
A positive integer
If $a$ and $b$ are integers, what is the result of $(a + b) × (a - b)$?
$a^2 - b^2$
What is the result of subtracting a positive integer from another positive integer?
A negative integer
If $a$ and $b$ are integers, what is the result of $(a - b) + (a + b)$?
$2a$
What is the consequence of not carrying over the extra value when multiplying?
The product will be incorrect
What is the purpose of finding the highest common factor (HCF) of two or more numbers?
To simplify fractions to their lowest terms
What is the consequence of dividing a number by a prime number in the process of prime factorization?
The quotient will be 1
What is the relationship between the least common multiple (LCM) and the highest common factor (HCF) of two or more numbers?
The LCM is always greater than the HCF
What is the purpose of calculating the rate in a problem?
To find the time required to complete a task
What is the process of expressing a number as the product of its prime factors?
Prime factorization
What is the formula to find the distance traveled given the speed and time?
Distance = Speed × Time
What is the purpose of finding the least common multiple (LCM) of two or more numbers?
To find the common denominator for adding fractions
What is the result of dividing a number by its highest common factor (HCF)?
The result is always 1
What is the purpose of using the formula Distance = Speed × Time?
To find the distance traveled given the speed and time
What is the ratio of hours worked to be used to divide the total amount to be shared in sharing based on work done?
The ratio of the hours worked by each person to the total hours worked
If a recipe requires 2 cups of flour to make 12 cookies, how many cups of flour will be needed to make 24 cookies?
4 cups
If two objects have dimensions in the ratio 2:3, what is the ratio of their areas?
4:9
If a quantity is increased by a factor of 2, what is the ratio of the new quantity to the original quantity?
2:1
If a car travels 120 miles in 2 hours, what is its speed in miles per hour?
60 miles per hour
If a discount of 20% is applied to an article marked at $100, what is the selling price?
$90
If a profit of 25% is made on an article sold at $120, what is the cost price?
$96
If a simple interest of $60 is earned on a principal of $1000 for 2 years, what is the rate of interest?
3%
If the absolute value of an integer is 5, what are its possible values?
5 or -5
If the product of two integers is negative, what can be said about their signs?
One is positive and the other is negative
What is the result of multiplying a positive integer by the product of a negative integer and a negative integer?
A positive integer
If $a + b = c$, then what is the value of $(-a) + (-b)$?
$-c$
What is the result of subtracting a negative integer from a positive integer?
A positive integer
If $a imes b = c$, then what is the value of $(-a) imes (-b)$?
$c$
What is the result of adding a positive integer and a negative integer with the same absolute value?
Zero
What is the property of integers that allows us to rearrange the numbers when adding or multiplying?
Commutative property
What is the result of multiplying a positive integer by a negative integer and then adding a positive integer?
A negative integer
If $a imes (b + c) = d$, then what is the value of $a imes b + a imes c$?
$d$
What is the result of subtracting a positive integer from a negative integer?
A negative integer
What is the result of multiplying two integers with the same sign?
A positive integer
What is the result of multiplying two fractions with the same denominator?
A fraction with a numerator equal to the product of the numerators and a denominator equal to the product of the denominators
What is the purpose of finding the least common multiple (LCM) of the denominators when adding or subtracting fractions?
To find the common denominator
What is the result of dividing a fraction by another fraction?
A fraction with a numerator equal to the product of the numerators and a denominator equal to the product of the denominators
What is the purpose of simplifying fractions?
To reduce the fraction to its simplest form
What is the result of converting a fraction to a decimal?
A decimal number
What is the purpose of converting a fraction to a percentage?
To express the fraction as a part of a whole
What is the result of finding the equivalent fractions of a given fraction?
A fraction with the same value
What is the purpose of using the concept of equivalent fractions?
To add or subtract fractions
What is the result of multiplying a fraction by its reciprocal?
A fraction with a value of 1
What is the result of dividing a fraction by its reciprocal?
A fraction with a value of 1
What is the correct way to divide a decimal fraction by another decimal fraction?
Convert only the divisor to a whole number, then divide and adjust the result.
What is the purpose of multiplying by powers of 10 when multiplying decimal fractions?
To eliminate the decimals from the numbers.
What is the correct way to add decimal fractions?
Align the decimal points, then add corresponding digits.
What is the formula to find the comparison as a percentage?
(Part ÷ Whole) × 100
What is the purpose of aligning decimal points when adding or subtracting decimal fractions?
To ensure the correct placement of the decimal point in the result.
What is the correct way to solve problems involving decimal fractions?
Use the correct techniques for addition, subtraction, multiplication, and division of decimal fractions.
What is the purpose of adjusting the result when multiplying decimal fractions?
To adjust the decimal place in the result to the correct position.
What is the correct way to divide a total amount by a certain number of people?
Convert the total amount to a decimal, then divide.
What is the purpose of converting the divisor to a whole number when dividing decimal fractions?
To eliminate the decimals from the divisor.
What is the correct way to solve weight and cost calculations involving decimal fractions?
Multiply the volume by the weight per unit volume, then multiply by the cost per unit weight.
What is the result of dividing a fraction by its reciprocal?
1
What is the formula to convert a fraction to a percentage?
( \frac{a}{b} \times 100 )
What is the process of finding a fraction of a fraction?
Multiplying the fractions
What is the formula to simplify a fraction?
( \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} )
What is the formula to find the percentage change between two values?
( \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 )
What is the formula to convert a percentage to a fraction?
( \frac{\text{Percentage}}{100} )
What is the formula to find the part of a whole given a percentage?
( \left( \frac{\text{Percentage}}{100} \right) \times \text{Whole} )
What is the formula to find the increased value of a number given a percentage increase?
( \text{Original Number} + \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )
What is the formula to find the decreased value of a number given a percentage decrease?
( \text{Original Number} - \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )
What is the formula to find the percentage of a quantity given the part and the whole?
( \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 )
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
