Review Exercises
Use the Language of Algebra
Identify Multiples and Factors
Use the divisibility tests to determine whether 180 is divisible by 2, by 3, by 5, by 6, and by 10.
Find the prime factorization of 252.
In the following exercises, simplify each expression.
Evaluate an Expression
In the following exercises, evaluate the following expressions.
When ⓐ ⓑ ⓒ
Simplify Expressions by Combining Like Terms
In the following exercises, simplify the following expressions by combining like terms.
Translate an English Phrase to an Algebraic Expression
In the following exercises, translate the phrases into algebraic expressions.
ⓐ the sum of and
ⓑ the product of and
ⓒ twelve more than
ⓓ less than
Dushko has nickels and pennies in his pocket. The number of pennies is four less than five times the number of nickels. Let represent the number of nickels. Write an expression for the number of pennies.
Integers
Simplify Expressions with Absolute Value
In the following exercise, fill in or for each of the following pairs of numbers.
In the following exercises, simplify.
Add and Subtract Integers
In the following exercises, simplify each expression.
Multiply and Divide Integers
In the following exercise, multiply or divide.
Simplify and Evaluate Expressions with Integers
In the following exercises, simplify each expression.
ⓐ ⓑ
For the following exercises, evaluate each expression.
when
Translate English Phrases to Algebraic Expressions
In the following exercises, translate to an algebraic expression and simplify if possible.
ⓐ the difference of 17 and ⓑ subtract 17 from
Use Integers in Applications
In the following exercise, solve.
Temperature On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau?
Fractions
Simplify Fractions
In the following exercises, simplify.
Multiply and Divide Fractions
In the following exercises, perform the indicated operation.
Add and Subtract Fractions
In the following exercises, perform the indicated operation.
ⓐ ⓑ
Use the Order of Operations to Simplify Fractions
In the following exercises, simplify.
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
when
and
Decimals
Round Decimals
Round to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
Add and Subtract Decimals
In the following exercises, perform the indicated operation.
Multiply and Divide Decimals
In the following exercises, perform the indicated operation.
Convert Decimals, Fractions and Percents
In the following exercises, convert each decimal to a fraction.
In the following exercises, convert each fraction to a decimal.
In the following exercises, convert each decimal to a percent.
Simplify Expressions with Square Roots
In the following exercises, simplify.
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercise, list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers for each set of numbers
Locate Fractions and Decimals on the Number Line
In the following exercises, locate the numbers on a number line.
ⓐ ⓑ
Properties of Real Numbers
Use the Commutative and Associative Properties
In the following exercises, simplify.
Use the Properties of Identity, Inverse and Zero
In the following exercises, simplify.
Simplify Expressions Using the Distributive Property
In the following exercises, simplify using the Distributive Property.