512 Questions
What is the purpose of rounding off numbers in calculations?
To simplify calculations and estimate results
What is the process of adjusting the rounded results to correct for the error introduced by rounding called?
Compensating
What is the method of adding numbers in which numbers are broken down into parts and added separately?
Expanded notation
What is the process of expressing a number as the product of its prime factors?
Prime factorization
What is the technique used in subtraction when the top digit is smaller than the bottom digit in a column?
Borrowing
What is the method of multiplication in which each digit is multiplied separately and the partial products are summed?
Multiplication in parts
What is the largest number that divides two or more numbers without leaving a remainder?
Highest common factor
Which of the following is a characteristic of a prime number?
It has exactly two distinct positive divisors
What is the term for the leftover value in long division?
Remainder
Why is rounding off to the nearest thousand used in estimating products?
To simplify calculations and get a quick approximation
What is the formula to calculate distance when given speed and time?
Distance = Speed × Time
What is the term for the process of breaking down numbers into smaller manageable parts in long division?
Step-by-step division
How do you find the LCM of two numbers?
Take the highest power of each prime factor
What is the purpose of finding the HCF in fractions?
To simplify fractions to their lowest terms
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 the benefit of using multiples of a thousand when estimating products?
It makes calculations faster and easier to simplify
What is the definition of a multiple of a number?
The product of that number and an integer
How do you determine if a number is prime?
Check if it can be divided evenly by any prime numbers smaller than its square root
What is the purpose of finding the prime factorization of a number?
To express a composite number as a product of prime factors
What is the definition of a composite number?
A natural number greater than 1 that can be formed by multiplying two smaller natural numbers
If a recipe serves 12 people and you want to serve 18 people, by what factor do you need to scale up the ingredients?
1.5
To decrease the quantity of an ingredient by 25% in a recipe, what operation do you need to perform?
Multiply by 0.75
What is the selling price of an article marked at $100 with a 20% discount?
$90
If the cost price of an article is $50 and the selling price is $60, what is the profit percentage?
20%
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the absolute value of the integer -5?
5
What is the product of two negative integers?
A positive integer
What is the result of cubing a negative integer?
A negative integer
If the distance traveled by a car in 2 hours is 120 km, what is its speed?
80 km/h
If the principal amount is $1000, the rate of interest is 5%, and the time is 2 years, what is the simple interest?
$200
What is the commutative property of addition?
a + b = b + a
Which of the following properties does not apply to subtraction and division?
The commutative property of addition and multiplication
What is the purpose of using a summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is the distributive property of multiplication over subtraction?
a × (b - c) = a × b - a × c
What is the purpose of estimating in calculations with whole numbers?
To try to get close to an answer without doing precise calculations
What is the associative property of addition?
(a + b) + c = a + (b + c)
What is the additive property of 0?
a + 0 = a
What is the benefit of using the commutative and associative properties in calculations?
It simplifies the calculation and saves time
What is the result of adding a positive integer to its additive inverse?
Zero
What is the product of a positive integer and a negative integer?
Negative
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the commutative property of addition?
Changing the order of numbers does not change the sum
What is the result of adding a negative integer to a positive integer?
Depends on the specific integers
What is the distributive property of multiplication?
Multiplication distributes over both addition and subtraction
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the result of dividing a positive integer by a negative integer?
A negative integer
What is the cube root of a negative integer?
Negative
What is the result of multiplying a positive integer and a negative integer?
Always negative
What is the purpose of the distributive property?
To distribute multiplication over addition and subtraction
What is the result of raising a negative integer to an even power?
Always positive
What is the formula for multiplying powers with the same base?
a^m × a^n
What is the result of subtracting a negative integer from a positive integer?
The result is increased by the value of the negative integer
What property of integers states that the order of the numbers does not change the sum?
Commutative Property
What is the result of squaring a negative fraction?
The result is always positive
What is the result of multiplying an integer by its additive inverse?
Zero
Which property of integers states that changing the grouping of numbers does not change the product?
Associative Property
What is the purpose of scientific notation?
To express large numbers as the product of a number between 1 and 10 and a power of 10
What is the result of adding zero to any integer?
The original integer
What is the result of dividing a positive integer by a negative integer?
The result is always negative
What is the property of exponents that states a^m × a^n = a^(m+n)?
Product of Powers
What is the result of subtracting an integer from a smaller integer?
A negative number
What is the result of multiplying two integers with different signs?
A negative number
What is the result of raising a number to the power of zero?
The result is always one
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the formula for equivalent fractions?
$\frac{a \times k}{b \times k} = \frac{a}{b}$
What property of integers allows us to multiply a number by a sum of numbers?
Distributive Property
What is the result of multiplying an integer by one?
The original integer
When adding or subtracting decimal fractions, what is the first step?
Add or subtract the digits as you would with whole numbers
When multiplying decimal fractions, why do we convert them to whole numbers?
To eliminate the decimals
When dividing a decimal fraction, what do we do to the divisor?
Multiply it by a power of 10
What is the property of integer operations that allows us to add and subtract in any order?
Commutative Property
What is the symbol used to indicate that one integer is greater than another?
>
What is the purpose of converting decimals to whole numbers in multiplication?
To eliminate the decimals
When dividing decimal fractions, what do we do to the result?
Adjust the decimal place
What is the property of multiplication that states that the order of the factors does not change the product?
Commutative Property
Which of the following statements is true about adding and subtracting integers?
Adding a positive integer increases the value, and subtracting a negative integer increases the value.
What is the result of adding an integer and its additive inverse?
Zero
What is the term for an equation where all the numbers are known?
Closed Number Sentence
What is the purpose of the Associative Property of integer operations?
To add and subtract integers in any order
What is the formula to calculate the nth term of a sequence with a constant difference?
T_n = T_1 + (n - 1) * d
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the property of integer operations that allows integers to be added and subtracted in any order?
Associative Property
What is the term for the negative counterpart of an integer that, when added to the integer, results in zero?
Additive Inverse
What is the formula to calculate the nth term of a sequence with a constant ratio?
T_n = T_1 * r^(n-1)
What is the term for a sequence that follows a linear pattern?
Arithmetic Sequence
What is the formula to calculate the nth term of a linear sequence?
T_n = a * n + b
What is the purpose of using the additive inverse of an integer in a statement?
To subtract the integer from another value
What is the purpose of finding the common denominator when adding or subtracting fractions?
To enable the addition or subtraction of fractions with different denominators
What is the result of multiplying the numerators and denominators together when multiplying fractions?
A new fraction with the product of the numerators and denominators
What is the process of dividing both the numerator and denominator of a fraction by their greatest common divisor?
Simplifying the fraction
What is the formula to convert a fraction to a percentage?
(a/b) × 100
What is the term for a fraction that represents a part of a whole that is divided into 10 equal parts?
Tenth
What is the result of multiplying a fraction by its reciprocal?
1
What is the purpose of finding the equivalent fractions?
To represent the same value in different forms
What is the formula to add or subtract fractions with different denominators?
(a/b) + (c/d) = (a×d + b×c)/(b×d)
What is the term for a fraction that combines a whole number and a fraction?
Mixed number
What is the purpose of converting a fraction to a decimal?
To make calculations easier
What is the formula to calculate the reciprocal of a fraction?
a/b = b/a
What is the formula to calculate the product of two fractions?
(a/b) × (c/d) = (a × c)/(b × d)
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 convert a percentage to a fraction?
Fraction = Percentage ÷ 100
What is the formula to find the percentage of a given number?
Percentage of a number = (Percentage/100) × Number
What is the formula to increase a number by a percentage?
Increased Value = Original Number + (Percentage/100) × Original Number
What is the formula to find the percentage change from an original value to a new value?
Percentage Change = ((New Value - Original Value)/Original Value) × 100
What is the concept of tenths, hundredths, and thousandths in fractions?
Fractions where the whole is divided into 10, 100, or 1000 parts
What is the definition of equivalent fractions?
Fractions that have different numerators and denominators but represent the same value
What is the process of finding an equivalent fraction in its simplest form?
Simplifying fractions
What is the formula to convert a mixed number to an improper fraction?
Improper Fraction = (Whole Number × Denominator) + Numerator
What is the definition of equivalent algebraic expressions?
Different algebraic expressions that simplify to the same value
How do 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 definition of like terms in algebraic expressions?
Terms that have the same variable(s) raised to the same power
What is the purpose of using the distributive property in algebra?
To expand algebraic expressions
What is the definition of a product expression in algebra?
An expression that involves multiplication as the last step
How do you simplify an algebraic expression involving division?
Distribute the division across terms
What is the purpose of using common denominators in adding or subtracting fractions?
To add or subtract fractions with different denominators
What is the definition of factoring in algebra?
Expressing an algebraic expression as a product of its factors
What is the formula for the nth triangular number?
T_n = n * (n + 1) / 2
What type of pattern is represented by the equation T_n = T_1 + (n - 1) * d?
Arithmetic progression
Which of the following quantities is an example of a constant quantity?
The number of fingers on your hands
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 purpose of a flow diagram?
To show the relationship between input and output numbers
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the formula for the nth square number?
T_n = n^2
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
What is the purpose of finding the relationship between variables?
To identify the variables that influence each other
What is the benefit of using flow diagrams to represent calculations?
It illustrates the calculation process and relationships between numbers
Which property states that the order of numbers in addition or multiplication does not change the result?
Commutative Property
What is the purpose of using the distributive property in calculations?
To simplify complex multiplications
What is the result of adding a positive integer to its additive inverse?
Zero
Which of the following properties does not apply to subtraction and division?
Commutative Property
What is the purpose of using a summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the purpose of estimating in calculations with whole numbers?
To get close to an answer without doing precise calculations
What is the associative property of addition?
Grouping of numbers in addition does not change the result
What is the process of dividing a number into its prime factors?
Prime Factorization
What is the term for the smallest multiple that two or more numbers have in common?
Least Common Multiple (LCM)
What is the characteristic of a prime number?
It has only two distinct positive divisors: 1 and itself
What is the process of calculating the time required to complete a task based on the rate?
Calculating Time Based on Rate
What is the term for the largest number that divides two or more numbers without leaving a remainder?
Highest Common Factor (HCF)
What is the method of describing the relationship between quantities in patterns?
Describing Patterns
What is the term for the product of a number and an integer?
Multiple
What is the process of sharing a total amount based on the ratio of hours worked?
Sharing Based on Work Done
What is the term for a natural number greater than 1 that is not prime?
Composite Number
What is the method of finding the prime factors of a number?
Start by dividing the number by the smallest prime number
What is the advantage of using multiples of a thousand when estimating products?
To simplify the calculation
What is the purpose of compensating in rounding off numbers?
To correct for the error introduced by rounding
What is the method of adding numbers in which numbers are aligned by their place values?
Column Addition
What is the technique used in subtraction when the top digit is smaller than the bottom digit in a column?
Borrowing Technique
What is the process of breaking down numbers into smaller manageable parts in long division?
Step-by-Step Division
What is the method of multiplication in which each digit is multiplied separately?
Multiplication in Parts
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of using the distributive property in multiplication?
To simplify the calculation
What is the benefit of using the commutative and associative properties in calculations?
To simplify the calculation
What is the purpose of scaling quantities in recipes?
To increase or decrease the number of servings
How do you calculate the selling price of an article with a marked price of $100 and a 20% discount?
Multiply 100 by 0.2 and subtract from 100
What is the result of multiplying two negative integers?
A positive integer
What is the purpose of comparing ratios in shapes?
To determine which shapes are more similar
What is simple interest calculated as?
Principal × Rate × Time
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of calculating profit percentage?
To determine the profit made from selling an article
What is the result of dividing a positive integer by a negative integer?
A negative integer
What is the purpose of calculating the absolute value of an integer?
To find the distance between the number and zero on the number line
What is the result of cubing a negative integer?
A negative integer
What is the result of adding a positive integer and its additive inverse?
0
What is the property that allows the flexibility in the order of integers in addition and subtraction?
Commutative property
What is the result of multiplying two negative integers?
A positive integer
What is the purpose of the additive inverse in integer operations?
To find the sum of zero
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the cube root of a negative integer?
A negative integer
What is the result of adding an integer and its multiplicative inverse?
1
What is the property that allows the flexibility in the order of integers in multiplication?
Commutative property
What is the result of dividing a positive integer by a negative integer?
A negative integer
What is the purpose of the commutative property in integer operations?
To multiply integers in any order
What is the formula to add two fractions a/b and c/d?
(a * d + b * c)/(b * d)
What is the formula to simplify a fraction a/b?
(a ÷ GCD(a, b))/(b ÷ GCD(a, b))
What is the formula to multiply two fractions a/b and c/d?
(a * c)/(b * d)
What is the formula to divide a fraction a/b by another fraction c/d?
(a * d)/(b * c)
What is the formula to convert a fraction a/b to a decimal?
a ÷ b
What is the formula to convert a fraction a/b to a percentage?
(a ÷ b) × 100
What is a mixed number?
A combination of a whole number and a fraction
What is the result of multiplying a positive integer and a negative integer?
Negative
What is an equivalent fraction?
A fraction with the same value but different numerator and denominator
What is the purpose of the distributive property of multiplication?
To multiply integers over addition and subtraction
What is the result of raising a number to the power of zero?
1
What is the purpose of finding the LCM of the denominators when adding or subtracting fractions?
To convert the fractions to have a common denominator
What is the formula to find a fraction of a fraction?
(a × c)/(b × d)
What is the product of two negative integers?
Positive
What is the result of subtracting a positive integer from its additive inverse?
Negative
What is the purpose of exponents in exponential form?
To represent a number as a product of the same integer
What is the result of adding a positive integer to its additive inverse?
Zero
What is the law of exponents that states a^m × a^n = a^(m+n)?
Product of Powers
What is the result of dividing a positive integer by a negative integer?
Negative
What is the result of squaring a fraction?
A new fraction with a squared numerator and denominator
Which property states that the order of the numbers does not change the product?
Commutative Property
What is the result of multiplying a number by its additive inverse?
0
Which property states that changing the grouping of numbers does not change the sum?
Associative Property
What is the purpose of the distributive property?
To multiply a number by a sum of numbers
Which property states that adding zero to a number does not change the number?
Identity Property
What is the result of multiplying two negative integers?
A positive integer
Which property states that multiplying a number by one does not change the number?
Identity Property
What is the result of subtracting a negative integer from a positive integer?
A larger positive integer
Which property allows you to multiply a number by a sum of numbers?
Distributive Property
What is the result of adding a positive integer to its additive inverse?
Zero
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 method to simplify a fraction?
Dividing the numerator and denominator by their greatest common divisor
What is the symbol for percentage?
%
How do you convert a fraction to a percentage?
Multiply the fraction by 100
What is the process of finding the percentage of a given number?
Converting the percentage to a fraction and multiplying by the number
What is the formula to calculate the percentage change?
$$\left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$$
What is the process of increasing or decreasing a number by a percentage?
Multiplying the number by the percentage and then adding or subtracting
What is the purpose of comparing quantities using percentages?
To compare the quantities in a more meaningful way
What is the formula to convert a mixed number to an improper fraction?
$$a \frac{b}{c} = \frac{a \times c + b}{c}$$
What is the reciprocal of a fraction?
The fraction with the numerator and denominator swapped
What is the property of multiplication that states that the order of the factors does not change the product?
Commutative Property
What is the result of adding a negative integer to its additive inverse?
Zero
What is the formula for the nth term of a sequence with a constant ratio?
Tn = T1 ⋅ r^(n-1)
What is the purpose of using the distributive property of multiplication?
To multiply integers by another integer or a sum of integers
What is the result of subtracting a positive integer from a negative integer?
A negative integer
What is the property of addition that states that the order of the addends does not change the sum?
Commutative Property
What is the formula for the nth term of a sequence with a constant difference?
Tn = T1 + (n - 1) ⋅ d
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the purpose of using the additive inverse of an integer?
To find the opposite of an integer
When adding decimal fractions, what should you do first?
Align the decimal points and then add corresponding digits
What is the property of multiplication that states that the product of a number and a sum of values is equal to the sum of the products?
Distributive Property
What is the first step in multiplying decimal fractions?
Convert the decimal fractions to whole numbers
To divide a decimal fraction by another decimal fraction, what should you do?
Convert the divisor to a whole number and then divide
What is the result of adding an integer and its additive inverse?
Zero
What is the property of integer operations that allows you to add integers in any order?
Commutative property of addition
What is the term for an equation where all the numbers are known?
Closed number sentence
What is the property of multiplication that states that the order of multiplication does not change the product?
Commutative property of multiplication
When comparing integers, what symbol is used to indicate that one integer is greater than another?
>
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the purpose of using the commutative and associative properties in calculations?
To simplify calculations
What is the definition of equivalent fractions?
Fractions that have different numerators and denominators but represent the same value
What is the process of finding an equivalent fraction in its simplest form?
Simplifying fractions
What is the method to convert decimals to fractions?
Write the decimal as a fraction with a denominator of a power of 10 and then simplify
What is the definition of equivalent algebraic expressions?
Different algebraic expressions that simplify to the same value
What is the method to identify equivalent algebraic expressions?
Using the distributive property
What is the purpose of simplifying algebraic expressions?
To combine like terms
What is the formula to calculate the number of elements in the nth position of a square number pattern?
T_n = n^2
What is the formula to calculate the number of elements in the nth position of a triangular number pattern?
T_n = n(n+1)/2
What is the definition of like terms?
Terms that have the same variable(s) raised to the same power
What is the formula to calculate the number of elements in the nth position of a pattern that follows an arithmetic progression?
T_n = T_1 + (n - 1) * d
What is the distributive property of multiplication?
a(b + c) = ab + ac
What is the purpose of expanding algebraic expressions?
To multiply each term inside the parenthesis by the factor outside
What is an example of a constant quantity?
The number of fingers on your hands
What is an example of a variable quantity?
The number of calls you make
What is the purpose of combining like terms in algebraic expressions?
To simplify the expression
What is the purpose of a flow diagram?
To show the relationship between input and output numbers
What is an equivalent form in mathematics?
A different expression that represents the same value or relationship
What is the relationship between the number of houses to be built and the number of bricks required?
The more houses, the more bricks required
What is the relationship between the number of learners at a school and the number of classrooms needed?
The more learners, the more classrooms needed
What is the relationship between the number of matches in an arrangement and the number of triangles in the arrangement?
The more matches, the more triangles
What is the primary purpose of prime factorization?
To express a number as a product of its prime factors
What is the relationship between the factors of a number?
They come in pairs and multiply to give the original number
What is the purpose of the least common multiple (LCM)?
To find the common denominator for adding fractions
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 the highest common factor (HCF)?
To simplify fractions to their lowest terms
What is the characteristic of a prime number?
It has exactly two distinct positive divisors: 1 and itself
What is the purpose of finding the ratio of two quantities?
To compare two quantities, showing how many times one value contains or is contained within the other
What is the relationship between a multiple and a factor of a number?
A multiple is the product of that number and an integer
What is the purpose of calculating the rate of a quantity?
To describe how one quantity changes in relation to another
What is the purpose of finding the prime factorization of a number?
To express a number as a product of its prime factors
What is the property that states that changing the order of numbers in addition or multiplication does not change the result?
Commutative Property
What is the result of multiplying a number by 1?
The number remains the same
Which of the following properties is used to break down complex multiplications into simpler parts?
Distributive Property
What is the purpose of using the commutative and associative properties in calculations?
To simplify calculations
What is the primary benefit of using rounding off in calculations?
To simplify calculations and check the reasonableness of results
What is the result of adding a number to its additive inverse?
The result is 0
When using the column subtraction method, what should you do if the top digit is smaller than the bottom digit in a column?
Borrow from the next left column
What is the benefit of using the distributive property of multiplication over addition?
It simplifies calculations
What is the purpose of estimating in calculations with whole numbers?
To get a close approximation
What is the purpose of compensating in calculations involving rounding off?
To adjust for the errors introduced by rounding off
What is the result of multiplying a number by its additive inverse?
The product is always 0
What is the property that states that the order in which you add or multiply numbers does not affect the result?
Commutative Property
What is the primary benefit of using the multiplication in parts method?
To reduce the complexity of calculations
What is the purpose of using expanded notation in addition?
To simplify calculations
What is the term for the process of breaking down numbers into smaller manageable parts in long division?
Step-by-step division
What is the purpose of using the borrowing technique in subtraction?
To adjust for the difference between the top and bottom digits in a column
What is the primary benefit of using column addition in calculations?
To simplify calculations and reduce errors
What is the result of adding a negative integer to a positive integer?
The result depends on the values of the integers
What is the purpose of scaling quantities in a recipe?
To maintain the ratio of ingredients to the number of servings
How do you increase the quantity of an ingredient in a recipe?
Multiply the quantity by the factor needed to reach the desired ratio
What is the formula to calculate the discount amount?
Marked price × discount rate
What is the result of subtracting a positive integer from a negative integer?
A negative integer
What is the product of three negative integers?
A negative integer
What is the formula to calculate simple interest?
Principal × rate × time
What is the result of adding a positive integer and its additive inverse?
Zero
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the absolute value of an integer?
The distance between the number and zero on the number line
What is the result of dividing a positive integer by a negative integer?
A negative integer
What is the result of adding a positive integer to its additive inverse?
Zero
What is the product of a positive integer and a negative integer?
Always negative
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the cube root of a positive integer?
Always positive
What is the result of adding a negative integer to its additive inverse?
Zero
What is the property that allows flexibility in the order of addition and multiplication of integers?
Commutative property
What is the result of multiplying a negative integer by a negative integer?
Always positive
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the property that allows the multiplication of integers to be distributed over addition and subtraction?
Distributive property
What is the result of adding a positive integer and its additive inverse?
Zero
What is the property of integers that states that changing the order of the numbers does not change the sum?
Commutative Property
Which of the following properties states that changing the grouping of the numbers does not change the product?
Associative Property
What is the property of integers that states that multiplying any number by one does not change the value of that number?
Identity Property of Multiplication
What is the result of adding a positive integer to its additive inverse?
Zero
What is the property of integers that states that each integer has an additive inverse (negative counterpart) such that their sum is zero?
Additive Inverse Property
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the property of integers that states that multiplying a number by a sum of numbers is the same as multiplying each addend separately and then adding the products?
Distributive Property
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the property of integers that states that adding zero to any number does not change the value of that number?
Identity Property of Addition
What is the result of multiplying a positive integer and 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 dividing fractions?
\frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} × \frac{d}{c}
What is the process of finding a fraction of a fraction?
Multiplying the fractions together
What is the result of converting a fraction to a decimal?
A non-repeating decimal
What is the formula for converting a fraction to a percentage?
Percentage = \frac{a}{b} × 100
What is the term for fractions where the whole is divided into 10, 100, or 1000 equal parts?
Tenths, hundredths, and thousandths
What is the formula for adding or subtracting fractions with different denominators?
\frac{a}{b} + \frac{c}{d} = \frac{a × d + b × c}{b × d}
What is the purpose of finding the equivalent fractions?
To represent the same value in different forms
What is the formula for multiplying fractions?
\frac{a}{b} × \frac{c}{d} = \frac{a × c}{b × d}
What is the process of converting a mixed number to an improper fraction?
Multiplying the whole number by the denominator and then adding the numerator
When multiplying decimal fractions, what is the first step?
Convert the decimal fractions to whole numbers
When dividing decimal fractions, how is the divisor converted to a whole number?
By multiplying both the dividend and the divisor by the same power of 10
What is the purpose of adding or subtracting corresponding digits when adding or subtracting decimal fractions?
To align the decimal points
What is the property of integer operations that states that integers can be added and subtracted in any order?
Associative Property of Addition
What is the term for an equation where all the numbers are known?
Closed Number Sentence
What is the symbol used to indicate 'greater than' when comparing integers?
>
What is the property of multiplication that states that the order of multiplication does not change the product?
Commutative Property of Multiplication
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 technique used to determine the duration of saving or total savings?
Division of the total amount saved by the weekly savings amount
What is the purpose of multiplying the volume by the weight per unit volume when calculating weight?
To find the weight of an object
What is the formula for the nth triangular number?
$T_n = n(n + 1)/2$
What type of progression is represented by the formula $T_n = T_1 + (n - 1) \cdot d$?
Arithmetic progression
Which of the following quantities has a direct influence on the number of bricks required for a construction project?
Number of houses to be built
What is the term for the relationship between two variable quantities where one quantity is influenced by the other?
Influence
What is the purpose of a flow diagram in mathematics?
To show the calculation process and relationships between numbers
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the formula for the nth square number?
$T_n = n^2$
Which of the following quantities is a constant quantity?
Length of a school day
What is the term for the connection between two quantities where one quantity increases when the other quantity increases?
Direct relationship
What is the purpose of analyzing the input-output relationships in a flow diagram?
To determine the operators needed to complete the flow diagram
What is the process of finding an equivalent fraction in its simplest form?
Simplifying fractions
What is the term for algebraic expressions that yield the same value for all values of the variables?
Equivalent expressions
How do you convert a decimal to a fraction?
Write the decimal as a fraction with a denominator of a power of 10 and simplify
What is the purpose of using the distributive property in algebra?
To multiply a single term by each term within a parenthesis
What is the result of combining like terms in an algebraic expression?
A simplified expression
What is the process of expressing an algebraic expression as a product of its factors?
Factoring
What is the term for fractions that have different numerators and denominators but represent the same value?
Equivalent fractions
What is the purpose of using common denominators when adding or subtracting fractions?
To enable addition or subtraction of fractions
What is the result of applying the distributive property to an algebraic expression?
An expanded expression
What is the term for the process of multiplying a single term by each term within a parenthesis?
Distributive property
What is the formula to convert a fraction to a decimal?
Divide the numerator by the denominator
What is the formula to simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD)
What is the formula to find a percentage of a number?
(Percentage/100) × Number
What is the formula to convert a percentage to a fraction?
Percentage/100
What is the formula to find the percentage change?
(New Value - Original Value) ÷ Original Value × 100
What is the formula to find the increased value of a number by a percentage?
Original Number + (Percentage/100) × Original Number
What is the formula to find the decreased value of a number by a percentage?
Original Number - (Percentage/100) × Original Number
What is the value of $a^0$?
1
What is the formula to find the reciprocal of a fraction?
Swap the numerator and denominator
What is the result of multiplying a negative integer and a positive integer?
negative
What is the distributive property of multiplication?
a (b - c) = (a b) - (a c)
What is the formula to find a fraction of a fraction?
Multiply the fractions together
What is the formula to find the percentage of a part to a whole?
(Part/Whole) × 100
What is the result of subtracting a positive integer from its additive inverse?
0
What is the exponent in the expression $a^m \div a^n$?
m - n
What is the result of cubing a negative integer?
a negative integer
What is the result of adding a positive integer to its additive inverse?
0
What is the power of a product?
(ab)^m = a^m b^m
What is the result of multiplying a positive integer and a negative integer?
a negative integer
What is the result of dividing a positive integer by a negative integer?
a negative integer
What is the property of multiplication where the order of the factors does not change the product?
Commutative Property
What is the result of adding a negative integer to its additive inverse?
Zero
What is the property of multiplication that distributes over addition and subtraction?
Distributive Property
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the formula to find the nth term of a sequence with a constant ratio?
Tn = T1 * r^(n - 1)
What is the formula to find the nth term of a sequence with a constant difference?
Tn = T1 + (n - 1) * d
What is the purpose of using the commutative and associative properties in calculations?
To simplify calculations
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the purpose of using position to make predictions in a sequence?
To determine the formula for the sequence
What is the result of adding a positive integer to a negative integer?
The sum of the integers
What is the main advantage of using the column addition method?
It makes it easier to check the reasonableness of results
When using the borrowing technique in subtraction, what happens to the top digit in the column?
It is increased by 10
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values
What is the benefit of using multiples of a thousand when estimating products?
It helps to reduce the error in the estimate
What is the purpose of compensating in rounding off numbers?
To adjust for the error introduced by rounding
What is the main advantage of using the multiplication in parts method?
It helps to reduce the number of calculations required
What is the purpose of using the expanded notation method in addition?
To break down the numbers into their components
What is the benefit of using the step-by-step division method?
It breaks down the division into smaller manageable parts
What is the purpose of using the column subtraction method?
To align the numbers by their place values and subtract each column
What is the main advantage of using the rounding off method?
It helps to simplify the calculations
What is the key point about the commutative property of addition and multiplication?
Changing the order of numbers in addition or multiplication does not change the result.
What is the purpose of using the distributive property of multiplication?
To break down complex multiplications into simpler parts.
What is the associative property of addition used for?
To group numbers in a way that makes calculations easier.
What is the purpose of using the additive property of 0?
To show that adding 0 to a number does not change its value.
What is the benefit of using the commutative and associative properties in calculations?
It allows for more efficient and accurate calculations.
What is the purpose of estimating in calculations with whole numbers?
To get a rough estimate of an answer.
What is the key point about the multiplicative property of 1?
It states that multiplying a number by 1 does not change its value.
What is the benefit of using a summary table for multiplication?
It helps to practice and reinforce the multiplication of various numbers.
What is the main difference between multiples and factors of a number?
Multiples are numbers that can be divided by another number to produce a quotient, whereas factors are numbers that divide exactly into another number.
What is the result of adding a positive integer and its additive inverse?
Zero
What is the purpose of finding the prime factorization of a number?
To express a number as the product of its prime factors
What is the result of multiplying a positive integer and a negative integer?
A negative integer
What is the distributive property of multiplication over subtraction?
a × (b - c) = (a × b) - (a × c)
What is the relationship between the LCM and HCF of two numbers?
The LCM is always greater than the HCF
If a recipe serves 8 people and you want to serve 12 people, by what factor do you need to scale up the ingredients?
1.33
What is the process of expressing a number as the product of its prime factors called?
Prime factorization
What is the associative property of multiplication?
(a × b) × c = a × (b × c)
What is the selling price of an article marked at $120 with a 25% discount?
$90
If the cost price of an article is $40 and the selling price is $48, what is the profit percentage?
20%
What is the result of subtracting the additive inverse of an integer from itself?
Zero
What is the benefit of using the prime factorization of a number?
It helps to find the prime factors of a number
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the commutative property of multiplication?
a × b = b × a
What is the formula to calculate the distance when given speed and time?
Distance = Speed × Time
What is the result of multiplying a positive integer by a negative integer?
Negative
What is the product of two integers with opposite signs?
Always negative
What is the result of adding a positive integer to its additive inverse?
Zero
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the purpose of finding the LCM of two numbers?
To find the common denominator for adding fractions
What is the result of subtracting a positive integer from its additive inverse?
Zero
What is the benefit of using multiples of a thousand when estimating products?
It helps to find the approximate product
What is the result of cubing a negative integer?
Negative
What is the cube root of a negative integer?
Always negative
What is the identity property of addition?
a + 0 = a
What is the result of multiplying a negative integer by a negative integer?
Always positive
What is the result of dividing a positive integer by a negative integer?
A negative integer
If the distance traveled by a car in 3 hours is 180 km, what is its speed?
60 km/h
What is the purpose of finding the HCF of two numbers?
To simplify fractions to their lowest terms
What is the relationship between the rate and ratio of two quantities?
The rate is the ratio of two quantities
What is the result of subtracting a positive integer from its additive inverse?
The negative of the integer
If the principal amount is $1500, the rate of interest is 6%, and the time is 3 years, what is the simple interest?
$270
What is the result of adding a negative integer to a positive integer?
A negative integer
What is the result of adding a negative integer to a positive integer?
Depends on the integers
What is the result of adding a positive integer to its additive inverse?
Zero
What is the commutative property of addition?
a + b = b + a
What is the result of multiplying a negative integer by a negative integer?
Positive
What is the result of dividing a positive integer by a negative integer?
Always negative
What is the distributive property of multiplication?
a × (b + c) = (a × b) + (a × c)
What is the least common multiple (LCM) of the denominators of two fractions required for when adding or subtracting fractions?
The product of the denominators
What is the result of multiplying the numerators and denominators of two fractions together?
An equivalent fraction
What is the purpose of finding the greatest common divisor (GCD) of the numerator and denominator of a fraction?
To simplify the fraction
What is the result of dividing a fraction by another fraction?
An equivalent fraction
What is the formula for converting a fraction to a percentage?
$rac{a}{b} imes 100$
What is the term for a fraction where the whole is divided into 10 parts?
Tenth
What is the purpose of using equivalent fractions?
To add or subtract fractions
What is the result of the expression (2^3)^2?
2^8
What is the value of a in the equation a × (b - c) = (a × b) - (a × c)?
any integer
What is the formula for subtracting one fraction from another with different denominators?
$rac{a}{b} - rac{c}{d} = rac{a imes d - b imes c}{b imes d}$
What is the result of the expression (3^2) × (3^4)?
3^8
What is the result of multiplying a fraction by its reciprocal?
1
What is the value of a^0?
1
What is the formula for dividing a fraction by another fraction?
$rac{a}{b} \div rac{c}{d} = rac{a imes d}{b imes c}$
What is the result of the expression a^m ÷ a^n?
a^(m-n)
What is the result of the expression (2 × 3)^4?
2^4 × 3^4
What is the result of the expression (5^2)^3?
5^8
What is the result of the expression 2^3 × 2^4?
2^12
What is the result of the expression a^m × a^n?
a^(m+n)
What is the result of the expression (4^2)^3?
4^8
What is the primary concept involved in adding or subtracting decimal fractions?
Align the decimal points, then add or subtract corresponding digits.
What is the correct step to perform after multiplying two whole numbers obtained from decimal fractions?
Divide the result by the power of 10 used earlier.
What is the purpose of converting the divisor to a whole number in dividing decimal fractions?
To eliminate the decimals in the divisor.
What is the correct method for dividing a total amount by a certain number of people?
Convert the total amount to a decimal if necessary and divide.
What is the purpose of the commutative property of addition?
To allow for the addition of integers in any order.
What is the reciprocal of the fraction $\frac{a}{b}$?
$\frac{b}{a}$
What is the result of adding an integer to its additive inverse?
The result is always zero.
What is the result of multiplying the fractions $\frac{a}{b}$ and $\frac{c}{d}$?
$\frac{a \times c}{b \times d}$
What is the purpose of the associative property of addition?
To group integers in a specific order when adding multiple numbers.
What is the simplified form of the fraction $\frac{a}{b}$?
$\frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)}$
What is the result of multiplying a positive integer and a negative integer?
The result is always negative.
What is the purpose of the closed number sentence?
To represent an equation where all numbers are known.
What is the percentage equivalent to the fraction $\frac{a}{b}$?
$\frac{a}{b} \times 100$
What is the result of subtracting a positive integer from its additive inverse?
The result is always negative.
What is the fraction equivalent to the percentage $x$%?
$\frac{x}{100}$
What is the result of increasing a number by $x$%?
$\text{Original Number} + \frac{x}{100} \times \text{Original Number}$
What is the percentage change from $a$ to $b$?
$\left(\frac{b - a}{a} \right) \times 100$
What is the result of comparing quantities $a$ and $b$ using percentages?
$\left(\frac{a}{b} \right) \times 100$
What is the result of adding two decimal fractions $a$ and $b$?
$a + b$
What is the result of subtracting two decimal fractions $a$ and $b$?
$a - b$
What is the result of converting the fraction 3/4 into a decimal?
0.75
What is the process of finding an equivalent fraction in its simplest form by dividing the numerator and the denominator by their greatest common divisor?
Simplifying fractions
What is the property that allows us to multiply a single term by each term within a parenthesis?
Distributive property
What is the term for expressions that add terms together?
Sum expressions
What is the process of combining like terms to simplify expressions?
Simplifying algebraic expressions
What is the method of adding or subtracting fractions by converting them to equivalent fractions with a common denominator?
Finding common denominators
What is the term for expressing an algebraic expression as a product of its factors?
Factoring algebraic expressions
What is the property that allows us to rearrange terms in an algebraic expression?
Commutative property
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the term for the sequence of operations and can be written in different forms while remaining equivalent?
Algebraic expressions
If a × (b + c) = (a × b) + (a × c), what is the name of the property that is being demonstrated?
Distributive Property
What is the result of adding a negative integer to its additive inverse?
Zero
If a × b = b × a, what is the name of the property that is being demonstrated?
Commutative Property
What is the formula to find the nth term in a sequence with a constant difference?
Tn = T1 + (n - 1) × d
If a sequence has a constant ratio, what is the formula to find the nth term?
Tn = T1 × r^(n - 1)
What is the name of the property that states that integers can be added and subtracted in any order?
Associative Property
What is the result of multiplying a negative integer by a negative integer?
A positive integer
What is the result of adding a positive integer to its additive inverse?
Zero
What is the formula to find the nth term in a sequence with a linear pattern?
Tn = a × n + b
What is the purpose of using the distributive property of multiplication?
To simplify multiplication
What is the general formula for the number of elements in the nth position of a geometric pattern?
Tn = T1 · r^(n-1)
What is the relationship between the number of calls made and the airtime left on a cell phone?
The number of calls made has a direct influence on the airtime left
What is the characteristic of a pattern that follows an arithmetic progression?
The difference between consecutive terms is constant
What is the purpose of a flow diagram in mathematics?
To illustrate the calculation process and the connection between input and output numbers
What is the definition of equivalent forms in mathematics?
Different expressions that represent the same value
What is the relationship between the number of houses to be built and the number of bricks required?
The number of houses has a direct influence on the number of bricks required
What is the characteristic of a triangular number?
The number of elements in the nth position is given by Tn = n(n+1)/2
What is the relationship between the number of learners at a school and the number of classrooms needed?
The number of learners has a direct influence on the number of classrooms needed
What is the purpose of looking for connections between quantities in mathematics?
To find the relationships between variables
What is the characteristic of a pattern that follows a geometric progression?
The ratio of consecutive terms is constant
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