Review Exercises
Use the Language of Algebra
Use Variables and Algebraic Symbols
In the following exercises, translate from algebra to English.
Identify Expressions and Equations
In the following exercises, determine if each is an expression or equation.
Simplify Expressions with Exponents
In the following exercises, write in exponential form.
In the following exercises, write in expanded form.
In the following exercises, simplify each expression.
Simplify Expressions Using the Order of Operations
In the following exercises, simplify.
Evaluate, Simplify, and Translate Expressions
Evaluate an Expression
In the following exercises, evaluate the following expressions.
Identify Terms, Coefficients and Like Terms
In the following exercises, identify the terms in each expression.
In the following exercises, identify the coefficient of each term.
In the following exercises, identify the like terms.
Simplify Expressions by Combining Like Terms
In the following exercises, simplify the following expressions by combining like terms.
Translate English Phrases to Algebraic Expressions
In the following exercises, translate the following phrases into algebraic expressions.
the sum of and twice
the quotient of and
less than the product of and
Jack bought a sandwich and a coffee. The cost of the sandwich was more than the cost of the coffee. Call the cost of the coffee Write an expression for the cost of the sandwich.
The number of poetry books on Brianna’s bookshelf is less than twice the number of novels. Call the number of novels Write an expression for the number of poetry books.
Solve Equations Using the Subtraction and Addition Properties of Equality
Determine Whether a Number is a Solution of an Equation
In the following exercises, determine whether each number is a solution to the equation.
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- ⓑ
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- ⓑ
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Model the Subtraction Property of Equality
In the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.
Solve Equations using the Subtraction Property of Equality
In the following exercises, solve each equation using the subtraction property of equality.
Solve Equations using the Addition Property of Equality
In the following exercises, solve each equation using the addition property of equality.
Translate English Sentences to Algebraic Equations
In the following exercises, translate each English sentence into an algebraic equation.
The difference of and is equal to
The quotient of and is equal to
The sum of five times and is
Translate to an Equation and Solve
In the following exercises, translate each English sentence into an algebraic equation and then solve it.
less than is
The sum of and is
Mixed Practice
In the following exercises, solve each equation.
Find Multiples and Factors
Identify Multiples of Numbers
In the following exercises, list all the multiples less than for each of the following.
Use Common Divisibility Tests
In the following exercises, using the divisibility tests, determine whether each number is divisible by
Find All the Factors of a Number
In the following exercises, find all the factors of each number.
Identify Prime and Composite Numbers
In the following exercises, identify each number as prime or composite.
Prime Factorization and the Least Common Multiple
Find the Prime Factorization of a Composite Number
In the following exercises, find the prime factorization of each number.
Find the Least Common Multiple of Two Numbers
In the following exercises, find the least common multiple of each pair of numbers.
Everyday Math
Describe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.