Review Exercises
Introduction to Whole Numbers
Use Place Value with Whole Number
In the following exercises find the place value of each digit.
359,417
ⓐ 9 ⓑ 3 ⓒ 4 ⓓ 7 ⓔ 1
9,430,286,157
ⓐ 6 ⓑ 4 ⓒ 9 ⓓ 0 ⓔ 5
In the following exercises, name each number.
493,068
85,620,435
In the following exercises, write each number as a whole number using digits.
sixty-five thousand, nine hundred twelve
one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven
In the following exercises, round to the indicated place value.
Round to the nearest hundred.
ⓐ 25,846 ⓑ 25,864
In the following exercises, round each number to the nearest ⓐ hundred ⓑ thousand ⓒ ten thousand.
3,972,849
Identify Multiples and Factors
In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.
264
750
1080
Find Prime Factorizations and Least Common Multiples
In the following exercises, find the prime factorization.
115
2475
56
168
391
In the following exercises, find the least common multiple of the following numbers using the multiples method.
60, 75
In the following exercises, find the least common multiple of the following numbers using the prime factors method.
70, 84
Use the Language of Algebra
Use Variables and Algebraic Symbols
In the following exercises, translate the following from algebra to English.
In the following exercises, determine if each is an expression or an equation.
Simplify Expressions Using the Order of Operations
In the following exercises, simplify each expression.
In the following exercises, simplify
Evaluate an Expression
In the following exercises, evaluate the following expressions.
when
when
when
Simplify Expressions by Combining Like Terms
In the following exercises, identify the coefficient of each term.
In the following exercises, identify the like terms.
In the following exercises, identify the terms in each expression.
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 following phrases into algebraic expressions.
the sum of 9 and 1
the difference of and 3
the product of 9 and
Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let represent the cost of the blouse. Write an expression for the cost of the skirt.
Marcella has 6 fewer boy cousins than girl cousins. Let represent the number of girl cousins. Write an expression for the number of boy cousins.
Add and Subtract Integers
Use Negatives and Opposites of Integers
In the following exercises, order each of the following pairs of numbers, using < or >.
ⓐ
ⓑ
ⓒ
ⓓ
In the following exercises,, find the opposite of each number.
ⓐ ⓑ
In the following exercises, simplify.
In the following exercises, simplify.
when
ⓐ
ⓑ
Simplify Expressions with Absolute Value
In the following exercises,, simplify.
ⓐ ⓑ ⓒ
In the following exercises, fill in <, >, or = for each of the following pairs of numbers.
ⓐ
ⓑ
In the following exercises, simplify.
In the following exercises, evaluate.
ⓐ when
ⓑ when
Add Integers
In the following exercises, simplify each expression.
Subtract Integers
In the following exercises, simplify.
ⓐ ⓑ
ⓐ ⓑ
In the following exercises, simplify each expression.
Multiply Integers
In the following exercises, multiply.
Divide Integers
In the following exercises, divide.
Simplify Expressions with Integers
In the following exercises, simplify each expression.
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
when ⓐ ⓑ
When , evaluate:
ⓐ >ⓑ
when
when and
Translate English Phrases to Algebraic Expressions
In the following exercises, translate to an algebraic expression and simplify if possible.
ⓐ the difference of 15 and ⓑ subtract 15 from
the product of and the difference of
Use Integers in Applications
In the following exercises, solve.
Temperature The high temperature one day in Miami Beach, Florida, was . That same day, the high temperature in Buffalo, New York was . What was the difference between the temperature in Miami Beach and the temperature in Buffalo?
Checking Account Adrianne has a balance of in her checking account. She deposits $301 to the account. What is the new balance?
Visualize Fractions
Find Equivalent Fractions
In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
Simplify Fractions
In the following exercises, simplify.
Multiply Fractions
In the following exercises, multiply.
Divide Fractions
In the following exercises, divide.
In the following exercises, simplify.
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
the quotient of the difference of h and k, and .
Add and Subtract Fractions
Add and Subtract Fractions with a Common Denominator
In the following exercises, add.
In the following exercises, subtract.
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
when
ⓐ
ⓑ
when and
when
Decimals
Name and Write Decimals
In the following exercises, write as a decimal.
Nine and seven hundredths
Nine thousandths
In the following exercises, name each decimal.
5.01
0.381
Round Decimals
In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
3.6284
25.8449
Add and Subtract Decimals
In the following exercises, add or subtract.
Multiply and Divide Decimals
In the following exercises, multiply.
In the following exercises, divide.
Convert Decimals, Fractions, and Percents
In the following exercises, write each decimal as a fraction.
0.17
0.184
0.035
In the following exercises, convert each fraction to a decimal.
In the following exercises, convert each percent to a decimal.
9%
50%
125%
In the following exercises, convert each decimal to a percent.
0.15
0.008
2.2
The Real Numbers
Simplify Expressions with Square Roots
In the following exercises, simplify.
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.
ⓐ ⓑ 3.591
In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers.
In the following exercises, identify whether each number is rational or irrational.
ⓐ ⓑ
In the following exercises, identify whether each number is a real number or not a real number.
ⓐ ⓑ
In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.
Locate Fractions on the Number Line
In the following exercises, locate the numbers on a number line.
In the following exercises, order each of the following pairs of numbers, using < or >.
Locate Decimals on the Number Line
In the following exercises, locate on the number line.
2.7
In the following exercises, order each of the following pairs of numbers, using < or >.
Properties of Real Numbers
Use the Commutative and Associative Properties
In the following exercises, use the Associative Property to simplify.
In the following exercises, simplify.
Use the Identity and Inverse Properties of Addition and Multiplication
In the following exercises, find the additive inverse of each number.
ⓐ
ⓑ
ⓒ
ⓓ
In the following exercises, find the multiplicative inverse of each number.
ⓐ ⓑ ⓒ 2.1
Use the Properties of Zero
In the following exercises, simplify.
In the following exercises, simplify.
Simplify Expressions Using the Distributive Property
In the following exercises, simplify using the Distributive Property.
Systems of Measurement
1.1 Define U.S. Units of Measurement and Convert from One Unit to Another
In the following exercises, convert the units. Round to the nearest tenth.
A picture frame is 42 inches wide. Convert the width to feet.
A playground is 45 feet wide. Convert the width to yards.
Shamu weights 4.5 tons. Convert the weight to pounds.
How many tablespoons are in a quart?
Trinh needs 30 cups of paint for her class art project. Convert the volume to gallons.
Use Mixed Units of Measurement in the U.S. System.
In the following exercises, solve.
John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?
Every day last week Pedro recorded the number of minutes he spent reading. The number of minutes were 50, 25, 83, 45, 32, 60, 135. How many hours did Pedro spend reading?
Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?
Dalila wants to make throw pillow covers. Each cover takes 30 inches of fabric. How many yards of fabric does she need for 4 covers?
Make Unit Conversions in the Metric System
In the following exercises, convert the units.
Mount Everest is 8,850 meters tall. Convert the height to kilometers.
One cup of yogurt contains 13 grams of protein. Convert this to milligrams.
A bottle of water contained 650 milliliters. Convert this to liters.
Use Mixed Units of Measurement in the Metric System
In the following exerices, solve.
Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?
Selma had a 1 liter bottle of water. If she drank 145 milliliters, how much water was left in the bottle?
One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?
One ounce of tofu provided 2 grams of protein. How many milligrams of protein are provided by 5 ounces of tofu?
Convert between the U.S. and the Metric Systems of Measurement
In the following exercises, make the unit conversions. Round to the nearest tenth.
A college basketball court is 84 feet long. Convert this length to meters.
Lucas weighs 78 kilograms. Convert his weight to pounds.
A box of books weighs 25 pounds. Convert the weight to kilograms.
Convert between Fahrenheit and Celsius Temperatures
In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.
23° Fahrenheit
64° Fahrenheit
In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.
–5° Celsius
24° Celsius