512 Questions
What is the commutative property of addition?
a + b = b + a
Which of the following properties is not applicable to subtraction and division?
Commutative property
What is the associative property of multiplication?
(a × b) × c = a × (b × c)
What is the additive property of 0?
a + 0 = a
What is the purpose of using the distributive property of multiplication over addition?
To break down complex multiplications into simpler parts
How can the commutative and associative properties help in simplifying calculations?
By changing the order of numbers being added or multiplied
What is the purpose of estimating in calculations with whole numbers?
To get close to an exact answer without doing precise calculations
What is the purpose of a summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is the definition of a multiple of a number?
The product of a number and an integer.
What is the definition of a prime number?
A natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
What is the purpose of finding the least common multiple (LCM)?
To find a common denominator for adding fractions.
What is the process of expressing a number as the product of its prime factors?
Prime factorization
What is the definition of a composite number?
A natural number greater than 1 that can be formed by multiplying two smaller natural numbers.
What is the formula for calculating distance?
Distance = Speed × Time
What is the purpose of finding the highest common factor (HCF)?
To simplify fractions to their lowest terms.
How do you find the time required to process a certain amount based on a rate?
Divide the total amount by the rate.
What is the definition of a rate?
Describes how one quantity changes in relation to another.
What is the purpose of expressing a ratio?
To identify the relationship between quantities in patterns.
What is the result of adding a positive integer to its additive inverse?
Zero
What is the effect of subtracting a positive integer from a number?
It decreases the value
What is the product of a positive integer and a negative integer?
Negative
What property of integers allows flexibility in computation and simplification?
All of the above
What is the purpose of rounding off numbers in calculations?
To simplify calculations and make quick decisions
What is the result of adding a negative integer to a number?
It decreases the value
What is the method of breaking down numbers into parts and adding each part separately?
Expanded Notation
What is the symbol used to indicate 'greater than' in comparing integers?
>
What is the result of multiplying a positive integer and a positive integer?
Positive
What is the technique of rearranging parts to make subtraction easier by borrowing from higher place values?
Borrowing Technique
What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?
Multiplication in Parts
What is the result of dividing a positive integer by a negative integer?
Negative
What is the purpose of compensating in calculations?
To adjust for errors introduced by rounding
What is the purpose of the Distributive Property of integers?
To multiply integers over addition and subtraction
What is the result of subtracting a negative integer from a number?
It increases the value
What is the method of aligning numbers vertically by their place values and adding each column?
Column Addition
What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?
Long Division
What is the term for the leftover value when dividing a number?
Remainder
What is the method of subtracting numbers by aligning them by their place values and subtracting each column?
Column Subtraction
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values to the next column
What is the property of addition that states that changing the order of the numbers does not change the sum?
Commutative Property
What is the property of multiplication that states that changing the grouping of the numbers does not change the product?
Associative Property
What is the formula to calculate simple interest?
Interest = Principal × Rate × Time
What is the property of multiplication that states that multiplication distributes over addition?
Distributive Property
What is the result of subtracting a positive integer from another positive integer?
The result can be either positive or negative
What is the additive inverse of an integer?
The negative counterpart of the number
What is the result of adding two positive integers?
A positive sum
What is the process of dividing quantities in a ratio?
Sum the parts of the ratio, divide the total quantity by the sum of the parts, and multiply by the number of parts each entity should receive.
What is the marked price of an article if the selling price is $120 and the discount is 20%?
$150
What is the result of subtracting a larger integer from a smaller one?
A negative difference
What is the result of multiplying two integers with the same sign?
A positive product
What is the absolute value of -5?
5
What is the result of multiplying a positive integer and a negative integer?
The result is always negative
What is the formula for equivalent fractions?
$\frac{a \times k}{b \times k} = \frac{a}{b}$
What is the formula to calculate profit percentage?
Profit percentage = (Selling price - Cost price) / Cost price × 100
What is the purpose of finding equivalent fractions?
To compare fractions
What is the result of adding a positive integer and a negative integer?
The result can be either positive or negative
What is the result of multiplying a fraction by a non-zero number?
The value of the fraction remains unchanged
What is the cube of -2?
-8
What is the process of scaling quantities in a recipe?
Use the ratio of ingredients to the number of servings to scale up or down as needed.
What is the first step in multiplying decimal fractions?
Convert the decimals to whole numbers by multiplying by powers of 10
When dividing a total amount by a certain number of people, what is the first step?
Convert the total amount to a decimal if necessary
What is the purpose of the additive inverse in integer operations?
To find the sum of an integer and its negative counterpart
What is the result of adding an integer and its additive inverse?
Zero
What is the purpose of the commutative property of multiplication?
To ensure that the product of multiplication is always the same regardless of the order of the factors
What is the result of subtracting an integer from itself?
Zero
What is the purpose of converting the divisor to a whole number in division of decimal fractions?
To ensure that the divisor is a whole number
What is the result of adding an integer and its negative counterpart?
Zero
What is the purpose of adjusting the decimal point in the result of multiplication of decimal fractions?
To ensure that the decimal point is in the correct position
What is the purpose of using the associative property of addition in decimal operations?
To ensure that the order of addition does not change the result
What property of integers allows for flexibility in computation and simplification?
Distributive Property
What is the result of raising a number to the power of zero?
1
What is the first step in adding or subtracting fractions?
Find the least common multiple of the denominators
What is the product of a negative integer and a negative integer?
Positive
How do you multiply fractions?
Multiply the numerators and denominators together
What is the purpose of expressing large numbers in scientific notation?
To make numbers easier to read
What is the reciprocal of a fraction?
The same fraction with the numerator and denominator swapped
What is the result of cubing a fraction?
A new fraction where both the numerator and the denominator are cubed
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor
What is the result of multiplying a fraction by its reciprocal?
1
What is the Power of a Product rule?
(ab)^m = a^m × b^m
How do you convert a fraction to a decimal?
Divide the numerator by the denominator
What is the result of multiplying a positive integer and a positive integer?
Positive
What is the purpose of combining integers using the order of operations (PEMDAS/BODMAS)?
To simplify expressions
What is the purpose of finding the least common multiple of the denominators?
To add or subtract fractions with different denominators
What is the result of dividing a fraction by 1?
The original fraction
What is the result of subtracting a negative integer from a number?
Increases the value
What is the purpose of equivalent fractions?
To represent the same value in different forms
What is the result of adding a positive integer to its additive inverse?
No change in the value
How do you convert a fraction to a percentage?
Multiply the fraction by 100
In the sequence of square numbers, what is the formula for the nth term?
T_n = n^2
What is the relationship between the number of calls made and the airtime left on a cell phone?
Direct influence, as the number of calls affects the airtime left.
What is the formula for the nth term of triangular numbers?
T_n = n(n + 1)/2
What type of pattern does the formula T_n = T_1 + (n - 1) * d represent?
Arithmetic progression
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the purpose of a flow diagram?
All of the above
What type of relationship exists between the number of learners at a school and the number of classrooms needed?
Direct influence
What is the term for a variable quantity that is influenced by another variable quantity?
Influenced quantity
What is the formula for the nth term of a geometric progression?
T_n = T_1 * r^(n-1)
What is the formula for dividing a fraction by another fraction?
( \frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} × \frac{d}{c} )
What is the formula for simplifying a fraction?
( \frac{a}{b} = \frac{a ÷ GCD(a, b)}{b ÷ GCD(a, b)} )
What is the relationship between the number of matches in an arrangement and the number of triangles in the arrangement?
Direct influence, as more matches create more triangles
What is the formula for converting a fraction to a percentage?
( \text{Percentage} = \frac{a}{b} × 100 )
What is the formula for finding the percentage of a given number?
( \text{Percentage of a number} = \frac{\text{Percentage}}{100} × \text{Number} )
What is the formula for increasing a number by a percentage?
( \text{Increased Value} = \text{Original Number} + \frac{\text{Percentage}}{100} × \text{Original Number} )
What is the result of adding a negative integer to its additive inverse?
Zero
What is the formula for decreasing a number by a percentage?
( \text{Decreased Value} = \text{Original Number} - \frac{\text{Percentage}}{100} × \text{Original Number} )
What property of multiplication states that the order of the factors does not change the product?
Commutative Property
What is the formula for calculating the percentage change?
( \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} × 100 )
What is the formula for converting a percentage to a fraction?
( \text{Fraction} = \frac{\text{Percentage}}{100} )
What is the formula for the nth term of a sequence with a constant difference?
Tn = T1 + (n - 1) × d
What is the formula for finding a fraction of a fraction?
( \frac{a}{b} × \frac{c}{d} = \frac{a × c}{b × d} )
What is the purpose of using the additive inverses in integer operations?
To simplify calculations
What is the formula for adding decimal fractions?
Align the decimal points and add the numbers.
What is the relationship between adding a positive integer and subtracting its additive inverse?
They have the same effect
What is the formula for the nth term of a sequence with a constant ratio?
Tn = T1 × r^(n-1)
What is the result of subtracting a negative integer from a number?
An increase in the value
What is the purpose of using the distributive property of multiplication?
To simplify calculations involving multiplication and addition
What is the symbol used to indicate 'greater than' in comparing integers?
>
What is the formula for the nth term of a sequence following a linear pattern?
Tn = a × n + b
What is the process of finding an equivalent fraction in its simplest form?
Dividing the numerator and the denominator by their greatest common divisor (GCD)
Which of the following is an example of an equivalent decimal?
0.5 and 1/2
What is the purpose of combining like terms in algebraic expressions?
To simplify the expression
How can you convert a decimal to a fraction?
Write the decimal as a fraction with a denominator of a power of 10 and then simplify
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the purpose of using flow diagrams in algebra?
To represent the sequence of operations visually
What is the result of simplifying the expression 2(x + 3)?
2x + 6
What is the purpose of factoring algebraic expressions?
To express algebraic expressions as a product of their factors
What is the result of combining like terms in the expression 2x + 3x?
5x
What is the purpose of using the order of operations in algebra?
To follow a specific order when performing calculations
What is the purpose of the commutative property of addition?
To allow flexibility in adding numbers in any order
Which property allows us to multiply numbers in any order?
Commutative property
What is the purpose of the associative property of addition?
To allow flexibility in adding numbers when more than two numbers are involved
What is the purpose of using the distributive property of multiplication over addition?
To break down complex multiplication into simpler parts
What is the purpose of a summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is the purpose of estimating in calculations with whole numbers?
To get close to the answer without doing precise calculations
What is the additive property of 0?
a + 0 = a
What is the multiplicative property of 1?
a x 1 = a
What is the purpose of estimating products by rounding to the nearest thousand?
To simplify the calculation and get a quick approximation
What is the benefit of using the column addition method?
It helps to simplify the calculation by aligning numbers by their place values
What is the method of subtracting numbers by aligning them by their place values and subtracting each column?
Column subtraction
What is the purpose of compensating in calculations?
To correct for errors introduced by rounding
What is the method of breaking down numbers into parts and adding each part separately?
Expanded notation
What is the purpose of using the borrowing technique in subtraction?
To simplify the calculation by rearranging parts
What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?
Multiplication in parts
What is the main difference between a prime number and a composite number?
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, while a composite number can be formed by multiplying two smaller natural numbers.
What is the term for the leftover value when dividing a number?
Remainder
What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?
Long division
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 process of expressing a number as the product of its prime factors called?
Prime factorization.
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values to the next column
How do you determine if a number is prime?
Check if the number can be divided evenly by any prime numbers smaller than its square root.
A recipe for 4 servings requires 2 cups of flour. How many cups of flour are needed for 8 servings?
4 cups
What is the formula to calculate distance when given the speed and time?
Distance = Speed × Time.
A bicycle travels 60 km in 2 hours. What is its speed?
60 km/h
What is the selling price of an article marked at $150 with a 15% discount?
$127.50
What is the purpose of expressing a ratio?
To compare two quantities.
What is the result of multiplying (-3) by 4?
-12
What is the result of multiplying a positive integer and a negative integer?
Always negative.
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 absolute value of (-8)?
8
What is the result of adding 5 and (-3)?
2
What is the method of dividing quantities in a ratio called?
Ratios and proportions.
What is the result of dividing $120 by a ratio of 3:4?
$72
What is the term for the leftover value when dividing a number?
Remainder.
What is the profit percentage if the selling price is $120 and the cost price is $100?
20%
What is the cube of (-2)?
-8
What is the result of subtracting (-3) from 5?
8
What is the result of adding an integer to its additive inverse?
The result is zero.
What is the effect of subtracting a negative integer from a number?
The result is increased by the value.
What is the product of two negative integers?
The product is always positive.
What is the purpose of the distributive property of multiplication?
To simplify calculations involving multiple operations.
What is the result of adding two negative integers?
The result is always negative.
What is the purpose of the commutative property of addition?
To allow flexibility in the order of operations in addition.
What is the result of multiplying a negative integer by a positive integer?
The result is always negative.
What is the purpose of the associative property of addition?
To allow flexibility in the order of operations in addition.
What is the result of subtracting a positive integer from another positive integer?
The result depends on the values of the integers.
What is the result of multiplying two positive integers?
The result is always positive.
What is the purpose of the associative property of addition?
To ensure that the sum of the numbers remains the same when the grouping of the numbers is changed
What is the formula to find an equivalent fraction?
$\frac{a}{b} = \frac{a \times k}{b \times k}$
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the purpose of the additive inverse of an integer?
To find the sum of a number and its negative counterpart
What is the result of adding a positive integer and its additive inverse?
Zero
What is the property of multiplication that states that the product of two numbers remains the same even if the order of the numbers is changed?
Commutative property of multiplication
What is the distributive property of multiplication?
Multiplication distributes over addition and subtraction
What is the result of subtracting a positive integer from a negative integer?
A negative integer
What is the identity property of multiplication?
Multiplying a number by one results in the number
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the result of multiplying a positive integer and a negative integer?
Negative
Which of the following properties is true about multiplication?
All of the above
What is the result of raising a number to the power of zero?
One
What is the purpose of using exponential form?
To simplify calculations
What is the result of cubing a fraction?
A new fraction where both the numerator and the denominator are cubed
What is the purpose of using scientific notation?
To simplify calculations involving large or small numbers
What is the result of dividing a positive integer by a negative integer?
Negative
What is the purpose of the power of a product rule?
To simplify calculations involving multiplication
What is the result of squaring a fraction?
A new fraction where both the numerator and the denominator are squared
What is the purpose of the quotient of powers rule?
To simplify calculations involving division
What is the first step in adding or subtracting fractions?
Find the least common multiple of the denominators
What is the formula for multiplying fractions?
( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )
What is the purpose of simplifying fractions?
To reduce the fraction to its simplest form
How do you convert a fraction to a decimal?
By dividing the numerator by the denominator
What is the formula for converting a fraction to a percentage?
( \frac{a}{b} \times 100 )
What is the term for a fraction that represents a part of a whole divided into ten equal parts?
Tenth
What is the formula for dividing fractions?
( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} )
What is the purpose of equivalent fractions?
To represent the same value
What is the formula for finding a fraction of a fraction?
( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )
What is the formula for simplifying a fraction?
( \frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} )
What is the result of adding a negative integer to its additive inverse?
0
If $a$ and $b$ are integers, what is the result of $a × (b - c)$?
$a × b - a × c$
What is the formula to find a fraction of a fraction?
$$ rac{a}{b} \div rac{c}{d} = rac{a}{b} imes rac{c}{d} $$
What is the purpose of identifying the rule in a sequence of numbers?
To find the next term in the sequence
What is the result of subtracting a negative integer from a number?
An increase in the value
What is the method to 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?
$$ ext{Percentage} = rac{a}{b} imes 100 $$
If $a$ and $b$ are integers, what is the result of $a + (-b)$?
$a - b$
What is the purpose of using the formula $T_n = T_1 + (n - 1) × d$ in a sequence?
To determine the next term in the sequence
What is the method to find the percentage of a given number?
Converting the percentage to a fraction and then multiplying by the number
What is the result of adding a positive integer to a number?
An increase in the value
What is the formula to increase a number by a percentage?
$$ ext{Increased Value} = ext{Original Number} + \left( rac{ ext{Percentage}}{100} imes ext{Original Number} ight) $$
What is the purpose of using the formula $T_n = a × n + b$ in a sequence?
To determine the next term in a linear sequence
What is the formula to find the percentage change?
$$ ext{Percentage Change} = \left( rac{ ext{New Value} - ext{Original Value}}{ ext{Original Value}} ight) imes 100 $$
What is the result of subtracting a positive integer from a number?
A decrease in the value
What is the formula to convert a percentage to a fraction?
$$ ext{Fraction} = rac{ ext{Percentage}}{100} $$
What is the purpose of using the formula $T_n = T_1 × r^{(n-1)}$ in a sequence?
To determine the next term in a sequence with a constant ratio
What is the method to add decimal fractions?
Aligning the decimal points and adding the numbers
What is the formula to find the decreased value of a number by a percentage?
$$ ext{Decreased Value} = ext{Original Number} - \left( rac{ ext{Percentage}}{100} imes ext{Original Number} ight) $$
What is the formula to compare quantities using percentages?
$$ ext{Comparison as Percentage} = \left( rac{ ext{Part}}{ ext{Whole}} ight) imes 100 $$
When adding or subtracting decimal fractions, what is the correct step to follow?
Align the decimal points and then add or subtract corresponding digits.
What is the purpose of converting decimal fractions to whole numbers when multiplying?
To eliminate the decimals and perform the multiplication as with whole numbers
When dividing a decimal fraction by another decimal fraction, what is the correct step to follow?
Convert the divisor to a whole number by multiplying both numbers by a power of 10, then divide
What is the result of adding a positive integer to its additive inverse?
Zero
Which property of multiplication allows flexibility in computation and simplification?
Associative Property
What is the purpose of using the additive inverse in calculations?
To simplify calculations by adding opposite numbers
When comparing integers, what symbol is used to indicate 'greater than'?
>
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the purpose of using the commutative property of addition?
To simplify calculations by changing the order of the numbers
What is the result of subtracting a negative integer from a number?
A positive integer
What is the purpose of finding the greatest common divisor (GCD) in simplifying fractions?
To find an equivalent fraction in its simplest form
What is the result of applying the distributive property to the expression 2(x + 3)?
2x + 6
What is the purpose of converting a fraction to a decimal?
To perform calculations with fractions
What is the result of combining like terms in the expression 2x + 3x?
5x
What is the purpose of using the distributive property in algebraic expressions?
To multiply a single term by each term within a parenthesis
What is the result of expanding the expression 2(x - 3)?
2x - 6
What is the purpose of simplifying algebraic expressions?
To make calculations easier
What is the result of converting the decimal 0.5 to a fraction?
1/2
What is the purpose of using factoring in algebraic expressions?
To express an algebraic expression as a product of its factors
What is the result of simplifying the algebraic expression 2x + 4x?
6x
What is the formula for the nth triangular number?
Tn = n(n + 1)/2
What type of pattern is represented by the formula Tn = T1 + (n - 1) ⋅ d?
Arithmetic progression
What is the relationship between the number of calls made and the airtime left on a cell phone?
The more calls you make, the less airtime you have left.
What is the phrase used to describe different expressions that represent the same value or relationship?
Equivalent forms
What is the purpose of a flow diagram?
To show the calculations needed to produce output numbers from input numbers.
What type of quantities are age and the number of fingers on your hands?
Age is variable, and the number of fingers is constant.
What is the relationship between the number of identical houses to be built and the number of bricks required?
More houses require more bricks.
What is the purpose of identifying relationships between variables?
To find a specific value of one quantity linked to a value of the other quantity.
What type of diagram shows the calculations needed to produce output numbers from input numbers?
Flow diagram
What is the purpose of describing the relationship between input and output numbers?
To illustrate the calculation process and the connection between input and output numbers.
What is the result of adding 0 to a whole number?
The result is always equal to the original number
Which property allows us to regroup numbers when adding or multiplying three or more numbers?
Associative Property
What is the purpose of using the Distributive Property of multiplication over addition?
To break down complex multiplications into simpler parts
What is the result of multiplying a whole number by 1?
The result is always the original number
Why is estimating useful in calculations with whole numbers?
To get close to an answer without doing precise calculations
What is the purpose of using a summary table for multiplication?
To practice and reinforce multiplication facts
What is the result of multiplying a whole number by -1?
The result is always negative
What is the purpose of rounding off numbers in calculations?
To simplify complex calculations
What is the purpose of rounding off numbers in calculations?
To make calculations easier and faster
What is the method of breaking down numbers into parts and adding each part separately?
Expanded Notation
What is the result of subtracting a negative integer from a number?
The result is the same as adding the absolute value of the integer
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values to the next column
What is the method of aligning numbers vertically by their place values and adding each column?
Column Addition
What is the term for the leftover value when dividing a number?
Remainder
What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?
Long Division
What is the technique of rearranging parts to make subtraction easier by borrowing from higher place values?
Borrowing Technique
What is the method of subtracting numbers by aligning them by their place values and subtracting each column?
Column Subtraction
What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?
Multiplication in Parts
What is the purpose of scaling quantities in recipes?
To increase or decrease the quantity of ingredients based on the number of servings
How can you calculate the profit percentage of an item?
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 adding a positive integer and a negative integer?
Depends on the absolute values of the integers
How can you calculate the simple interest on an investment?
By multiplying the principal by the rate and time, and dividing by 100
What is the result of multiplying two negative integers?
Always positive
What is the result of adding a positive integer to its additive inverse?
Zero
How can you calculate the discount amount of an item?
By multiplying the marked price by the discount rate, and subtracting the discount from the marked price
What is the purpose of comparing ratios?
To determine which shapes or objects are more similar
What is the effect of subtracting a negative integer from a number?
It increases the value
How can you increase a quantity in a ratio?
By multiplying the quantity by the factor needed to reach the desired ratio
What is the product of a positive integer and a negative integer?
A negative integer
What property of integers allows flexibility in computation and simplification?
All of the above
What is the result of subtracting a negative integer from a number?
Always increases the value
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 result of multiplying a positive integer and a negative integer?
A negative integer
What is the result of multiplying a positive integer by -1?
A negative integer
Which of the following properties states that the order of the numbers does not change the sum in addition?
Commutative Property
What is the purpose of the Distributive Property of integers?
To simplify complex calculations
What is the purpose of the additive inverse in integer operations?
To find the sum of a number and its negative counterpart
What is the result of adding two positive integers?
A positive integer
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the result of subtracting a larger integer from a smaller one?
A negative integer
Which property allows multiplication to distribute over addition?
Distributive Property
What is the result of multiplying two integers with the same sign?
A positive integer
What is the result of adding two negative integers?
A negative integer
What is the result of dividing a positive integer by a negative integer?
A negative integer
Which property states that changing the grouping of numbers does not change the product in multiplication?
Associative Property
What is the result of multiplying a negative integer by -1?
A positive integer
Which property states that adding zero to any number does not change the value of that number?
Identity Property
What is the purpose of the absolute value of an integer?
To find the distance between the number and zero on the number line
What is the least common multiple (LCM) used for in adding or subtracting fractions?
Converting fractions to have a common denominator
What is the formula to simplify a fraction?
a / b = a ÷ GCD(a, b) / b ÷ GCD(a, b)
How do you convert a fraction to a decimal?
Divide the numerator by the denominator
What is the result of multiplying two fractions together?
The product of the numerators divided by the product of the denominators
How do you divide a fraction by another fraction?
Multiply the fraction by the reciprocal of the other fraction
What is the term for a fraction that represents a part of a whole?
Fraction of a fraction
What is the purpose of finding the greatest common divisor (GCD) in simplifying fractions?
To divide both the numerator and denominator by their GCD
What is the formula to convert a fraction to a percentage?
Percentage = (a / b) × 100
What is the term for a fraction that combines a whole number with a fraction?
Mixed number
What is the purpose of equivalent fractions?
To represent the same value even though they may look different
What is the purpose of finding the prime factorization of a number?
To express the number as a product of its prime factors
What is the difference between a prime number and a composite number?
A prime number has exactly two factors, while a composite number has more than two factors
What is the purpose of finding the highest common factor (HCF) of two numbers?
To simplify fractions to their lowest terms
How do you determine if a number is prime?
By checking if it can be divided evenly by any number smaller than its square root
What is the purpose of finding the least common multiple (LCM) of two numbers?
To find a common denominator for adding fractions
What is the formula for calculating distance?
Distance = Speed × Time
What is the purpose of expressing a ratio?
To compare two quantities
What is the result of dividing a number by its highest common factor (HCF)?
The result is always simplified
What is the purpose of finding the multiples of a number?
To identify the sequence of numbers formed by multiplying the number by an integer
What is the purpose of calculating the rate of a process?
To find the time required to complete the process
What is the formula to calculate a fraction of a fraction?
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
How do you simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD)
What is the formula to convert a fraction to a percentage?
$\frac{a}{b} \times 100$
What is the formula to find the percentage of a given number?
$\left(\frac{\text{Percentage}}{100}\right) \times \text{Number}$
How do you increase a number by a percentage?
Calculate the percentage of the number and add it to the original number
What is the formula to calculate percentage change?
$\left(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}}\right) \times 100$
What is the formula to convert a percentage to a fraction?
$\frac{\text{Percentage}}{100}$
How do you decrease a number by a percentage?
Calculate the percentage of the number and subtract it from the original number
What is the formula to find the reciprocal of a fraction?
$\frac{b}{a}$
What is the method of comparing quantities using percentages?
Divide the part by the whole and multiply by 100
When adding decimal fractions, what is the correct step to follow?
Align the decimal points and then add or subtract as with whole numbers
What is the purpose of converting decimal fractions to whole numbers in multiplication?
To eliminate the decimals
When dividing a total amount by a certain number of people, what is the correct step to follow?
Convert the total amount to a decimal if necessary and divide
What is the correct technique for multiplying decimal fractions?
Convert the decimals to whole numbers, multiply, and then adjust the decimal place
What is the correct technique for dividing decimal fractions?
Convert the divisor to a whole number, divide, and then adjust the quotient
What is the purpose of the associative property of addition?
To allow flexibility in the order of addition
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of the commutative property of multiplication?
To allow flexibility in the order of multiplication
What is the correct symbol for 'greater than' when comparing integers?
>
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the purpose of finding the equivalent fractions?
To compare the values of two fractions
What is the process of converting a decimal to a fraction?
Write the decimal as a fraction with a denominator of a power of 10 and then simplify
What is the distributive property used for in algebra?
To multiply a single term by each term within a parenthesis
What is the purpose of simplifying algebraic expressions?
To combine like terms and eliminate any constants
What is the result of multiplying two equivalent fractions?
A fraction with the same value as the original fractions
What is the purpose of using the order of operations?
To follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction
What is the result of simplifying a product expression?
A simplified expression with combined like terms
What is the purpose of factoring in algebra?
To express an algebraic expression as a product of its factors
What is the result of adding two equivalent decimals?
A decimal with the same value as the original decimals
What is the purpose of using flow diagrams in algebra?
To visualize the sequence of operations
What is the formula for calculating the nth triangular number?
$T_n = n(n+1)/2$
What is the relationship between the number of calls made and the airtime left on a cell phone?
The more calls made, the less airtime is left.
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the result of multiplying a negative integer and a negative integer?
Positive
What is the purpose of flow diagrams in mathematics?
To show the relationships between variables
What is the purpose of expressing a number in scientific notation?
To write the number as a product of a number between 1 and 10 and a power of 10
What is the result of squaring a fraction?
A new fraction where both the numerator and the denominator are squared
What is the formula for calculating the nth term of a pattern that follows a geometric progression?
$T_n = T_1 \cdot r^{(n-1)}$
What is the relationship between the number of learners at a school and the number of classrooms needed?
More learners require more classrooms.
What is the property of multiplication that states that multiplication distributes over addition and subtraction?
Distributive Property
What is the purpose of describing calculations in words?
To explain the reasoning behind a calculation
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of using the Laws of Exponents?
To simplify expressions
What is the formula for calculating the nth term of a pattern that follows an arithmetic progression?
$T_n = T_1 + (n-1)d$
What is the relationship between the number of matches in an arrangement and the number of triangles in the arrangement?
More matches can create more triangles in specific patterns.
What is the result of cubing a fraction?
A new fraction where both the numerator and the denominator are cubed
What is the purpose of using exponents?
To write a product of the same integer in a concise manner
What is the purpose of finding a specific value of one quantity linked to a value of another quantity?
To identify the connection between two quantities
What is the result of subtracting a negative integer from a number?
The number increases
What is the purpose of comparing numbers in scientific notation?
To compare the exponents and then the base numbers
What is the result of adding a positive integer to its additive inverse?
Zero
Which of the following statements is true about closed number sentences?
They contain only known constants
What is the purpose of using the distributive property of multiplication over addition?
To simplify calculations by breaking down multiplication into smaller parts
What is the formula for the nth term of a sequence with a constant difference?
T_n = T_1 + (n - 1) * d
What is the effect of adding a negative integer to a number?
It decreases the value
What is the purpose of using the associative property of addition?
To simplify calculations by allowing us to add numbers in any order
What is the result of subtracting a negative integer from a number?
It increases the value
What is the formula for the nth term of a sequence with a constant ratio?
T_n = T_1 * r^(n-1)
What is the purpose of using the commutative property of addition?
To simplify calculations by allowing us to add numbers in any order
What is the result of multiplying two integers with the same sign?
A positive integer
What is the result of multiplying a number by 1?
The result is always the number itself
What is the purpose of using the commutative property of addition?
To change the order of numbers in an addition problem
Which of the following properties does not apply to subtraction and division?
Commutative Property
What is the result of adding 0 to a number?
The result is always the number itself
What is the purpose of using the distributive property of multiplication over addition?
To break down complex multiplication into simpler parts
What is the benefit of using the associative property of multiplication?
It allows us to group numbers in different ways to simplify the problem
What is the purpose of estimating in calculations with whole numbers?
To get an approximate answer
What is the benefit of using a summary table for multiplication?
It helps in practicing and reinforcing multiplication of various numbers
What is the process of finding the prime factors of a number?
Prime factorization
What is the term for the leftover value when dividing a number?
Remainder
What is the purpose of finding the least common multiple (LCM) of two numbers?
To find the smallest multiple that two or more numbers have in common
What is the process of finding the highest common factor (HCF) of two numbers?
Find the lowest power of each prime factor that appears in the factorization of each number
What is the ratio of the number of hours worked by two people if they are paid $120 and $90, respectively?
4:3
What is the formula to calculate the distance traveled by an object?
Distance = Speed × Time
What is the purpose of calculating the time required to process a certain amount based on a rate?
To determine the time required to process a certain amount
What is the term for a natural number greater than 1 that can be formed by multiplying two smaller natural numbers?
Composite number
What is the process of dividing quantities in a given ratio?
Sharing based on work done
What is the term for describing how one quantity changes in relation to another?
Rate
What is the value of the expression 5 + (-5)?
0
What is the result of subtracting a negative integer from a positive integer?
A larger value
What is the product of a positive integer and a negative integer?
Always negative
What is the purpose of the distributive property of multiplication?
To simplify multiplication over addition and subtraction
What is the primary purpose of rounding off numbers in calculations?
To make calculations easier and faster
What is the result of adding a positive integer to its additive inverse?
Zero
What is the advantage of using the multiplication in parts method?
It helps in breaking down complex multiplications into simpler parts
What is the purpose of compensating in calculations?
To adjust for errors introduced by rounding
What is the effect of subtracting a positive integer from a number?
Decreases the value
What is the method of adding numbers by breaking down each number into its components?
Expanded Notation
What is the property of addition that allows flexibility in computation and simplification?
All of the above
What is the result of multiplying two negative integers?
A positive value
What is the term for the leftover value when dividing a number?
Remainder
What is the purpose of comparing integers using greater than or equal to?
To determine the relationship between two integers
What is the purpose of the borrowing technique in subtraction?
To make subtraction easier
What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?
Multiplication in Parts
What is the property of multiplication that allows changing the order of the numbers?
Commutative property
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values to the next column
What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?
Step-by-Step Division
What is the advantage of using the column addition method?
It helps in adding numbers with multiple digits
Which of the following properties of integers states that changing the order of the numbers does not change the sum?
Commutative Property
What is the result of adding a positive integer and its additive inverse?
Zero
Which of the following properties of integers allows flexibility in computation and simplification?
All of the above
What is the result of multiplying two integers with different signs?
A negative integer
What is the purpose of the Distributive Property of integers?
To simplify calculations involving multiplication
What is the result of adding two negative integers?
A negative integer
Which of the following properties of integers states that changing the grouping of the numbers does not change the product?
Associative Property
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the result of subtracting a positive integer from another positive integer?
A positive integer
What is the purpose of equivalent fractions?
To represent the same value in different ways
What is the purpose of scaling quantities in recipes?
To use the ratio of ingredients to the number of servings
How do you calculate the profit percentage?
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 adding a negative integer to a positive integer?
The result is positive if the positive integer is greater, otherwise negative
How do you find the value of one part when dividing quantities in a ratio?
By summing the parts of the ratio and dividing the total quantity by the sum of the parts
What is the formula for calculating simple interest?
Interest = Principal × Rate × Time
What is the result of multiplying two negative integers?
The result is always positive
What is the purpose of calculating the discount amount?
To find the selling price of an article
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the result of subtracting a positive integer from a negative integer?
The result is always negative
How do you calculate the selling price of an article after a discount?
By subtracting the discount amount from the marked price
What is the correct step to add or subtract decimal fractions?
Align decimal points and add or subtract as with whole numbers, then adjust the decimal point
How do you multiply decimal fractions?
Convert decimals to whole numbers, multiply, and then adjust the decimal place
What is the correct step to divide a decimal fraction by another decimal fraction?
Convert the divisor to a whole number, divide, and then adjust the decimal place
What is the purpose of converting decimal fractions to whole numbers in multiplication?
To simplify the calculation by eliminating decimals
What is the result of multiplying a positive integer by a negative integer?
A negative integer
What is the property of integers that allows flexibility in computation and simplification?
Commutative property of addition
What is the result of adding a positive integer to its additive inverse?
Zero
What is the effect of subtracting a positive integer from a number?
The result is the same as adding the additive inverse
What is the purpose of using exponential form in comparing and representing numbers?
To compare and represent numbers in a more concise and efficient manner
What is the symbol used to indicate 'greater than' in comparing integers?
>
What is the first step when adding or subtracting fractions with different denominators?
Find the least common multiple of the denominators
What is the result of multiplying a fraction by its reciprocal?
A fraction with a numerator of 1 and a denominator of 1
What is the result of multiplying two integers with different signs?
The result is always negative.
What is the purpose of using exponential form?
To simplify calculations involving powers.
What is the purpose of simplifying a fraction?
To reduce the fraction to its simplest form, where the numerator and denominator are as small as possible
What is the result of raising a number to the power of zero?
The result is always one.
What is the formula for converting a fraction to a percentage?
Percentage = (a / b) × 100
What is the formula for adding fractions with different denominators?
(a / b) + (c / d) = (a × d + b × c) / (b × d)
What is the rule for dividing powers with the same base?
Subtract the exponents.
What is the result of multiplying a fraction by a whole number?
A fraction with a numerator equal to the product of the original numerator and the whole number, and a denominator equal to the original denominator
What is the result of cubing a fraction?
The result is a new fraction where both the numerator and the denominator are cubed.
What is the purpose of dividing a fraction by its greatest common divisor?
To reduce the fraction to its simplest form, where the numerator and denominator are as small as possible
What is the purpose of scientific notation?
To express very large or very small numbers in a more compact form.
What is the formula for multiplying fractions?
(a / b) × (c / d) = (a × c) / (b × d)
What is the result of adding a positive integer to its additive inverse?
The result is always zero.
What is the law of exponents that states that any number raised to the power of zero is one?
Power of Zero.
What is the result of dividing a fraction by a whole number?
A fraction with a numerator equal to the original numerator divided by the whole number, and a denominator equal to the original denominator
What is the result of multiplying a positive integer and a negative integer?
The result is always negative.
What is the formula for finding a fraction of a fraction?
(a / b) × (c / d) = (a × c) / (b × d)
What is the result of subtracting a negative integer from another integer?
It has the same effect as adding its additive inverse.
What is the purpose of the commutative property of multiplication?
To allow flexibility in the order of multiplication.
What is the property of multiplication that states that changing the order of the numbers does not change the product?
Commutative Property
What is the formula for the nth term in a sequence with a constant difference?
Tn = T1 + (n - 1) × d
What is the result of adding an integer and its additive inverse?
It always equals 0.
What is the purpose of using the distributive property of multiplication?
To simplify calculations by breaking down multiplication into smaller parts.
What is the formula for the nth term in a sequence with a linear relationship?
Tn = a × n + b
What is the result of multiplying a positive integer and a negative integer?
It is always negative.
What is the effect of adding a positive integer to a number?
It always increases the value.
What is the property of integers that allows flexibility in computation and simplification?
Additive Inverses
What is the term for the leftover value when dividing a number?
Remainder
What is the formula for the number of elements in the nth position of a triangular number sequence?
Tn = n*(n+1)/2
What is the relationship between the number of identical houses to be built and the number of bricks required?
More houses require more bricks
What is the purpose of a flow diagram in mathematics?
To show the calculations needed to produce output numbers
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the formula to find a fraction of a fraction?
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
What is the formula for the number of elements in the nth position of a square number sequence?
Tn = n^2
What is the process of simplifying a fraction?
Dividing both the numerator and denominator by their greatest common divisor
What is the relationship between the number of learners at a school and the number of classrooms needed?
More learners require more classrooms
How do you convert a percentage to a fraction?
Write the percentage as a fraction with 100 as the denominator
What is the formula for the number of elements in the nth position of a T-shaped number sequence that follows an arithmetic progression?
Tn = T1 + (n - 1) * d
What is the relationship between the number of calls you make and the airtime left on your cell phone?
The more calls you make, the less airtime you have left
What is the formula to find the percentage change?
$\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$
What is the term for a variable quantity that is influenced by another variable quantity?
Dependent variable
What is the method of finding the percentage of a given number?
Convert the percentage to a fraction and multiply by the number
What is the purpose of finding the relationships between variables in mathematics?
To find a specific value of one quantity linked to a value of the other quantity
What is the formula to find the increased value of a number by a percentage?
$\text{Original Number} + \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right)$
What is the method of comparing quantities using percentages?
Divide the part by the whole and multiply by 100
What is the formula to find the decimal equivalent of a fraction?
Divide the numerator by the denominator
What is the method of converting a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100
What is the formula to find the reciprocal of a fraction?
$\frac{a}{b} = \frac{b}{a}$
What is the process of finding an equivalent fraction in its simplest form?
Simplifying fractions
Which of the following is an example of an equivalent algebraic expression?
2x + 3x
What is the purpose of using the distributive property of multiplication over addition?
To simplify algebraic expressions
What is the result of dividing a numerator by a denominator to convert a fraction to a decimal?
An equivalent decimal
What is the purpose of combining like terms in an algebraic expression?
To simplify the expression
What is the result of using the distributive property to expand a product expression?
A sum expression
What is the purpose of using factoring in algebraic expressions?
To simplify expressions
What is the result of converting a decimal to a fraction with a denominator of a power of 10?
An equivalent fraction
What is the purpose of using the associative property of multiplication in algebraic expressions?
To simplify expressions
What is the result of simplifying a quotient expression involving division?
A simplified algebraic expression
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