Review Exercises
Decimals
Name Decimals
In the following exercises, name each decimal.
0.8
0.007
−12.5632
Write Decimals
In the following exercises, write as a decimal.
three tenths
twenty-seven hundredths
negative twenty and three tenths
Convert Decimals to Fractions or Mixed Numbers
In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.
0.43
9.7
Locate Decimals on the Number Line
ⓐ 0.6
ⓑ −0.9
ⓒ 2.2
ⓓ −1.3
Order Decimals
In the following exercises, order each of the following pairs of numbers, using < or >.
0.2___0.15
−0.56____−0.562
Round Decimals
In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number.
4.8447
Decimal Operations
Add and Subtract Decimals
In the following exercises, add or subtract.
5.75+8.46
24−19.31
−6.4+(−2.9)
Multiply Decimals
In the following exercises, multiply.
(0.3)(0.7)
(−3.35)(−12.7)
Divide Decimals
In the following exercises, divide.
0.48÷6
$6.29÷12
1.65÷0.15
Use Decimals in Money Applications
In the following exercises, use the strategy for applications to solve.
Miranda got $40 from her ATM. She spent $9.32 on lunch and $16.99 on a book. How much money did she have left? Round to the nearest cent if necessary.
Jessie put 8 gallons of gas in her car. One gallon of gas costs $3.528. How much did Jessie owe for all the gas?
A pack of 16 water bottles cost $6.72. How much did each bottle cost?
Alice bought a roll of paper towels that cost $2.49. She had a coupon for $0.35 off, and the store doubled the coupon. How much did Alice pay for the paper towels?
Decimals and Fractions
Convert Fractions to Decimals
In the following exercises, convert each fraction to a decimal.
35
−1920
13
Order Decimals and Fractions
In the following exercises, order each pair of numbers, using < or >.
12___0.2
−78___−0.84
0.625___1320
In the following exercises, write each set of numbers in order from least to greatest.
23,1720,0.65
Simplify Expressions Using the Order of Operations
In the following exercises, simplify
4(10.3−5.8)
30÷(0.45+0.15)
52(0.5)+(0.4)2
Find the Circumference and Area of Circles
In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.
radius=6 in.
radius=733m
Solve Equations with Decimals
Determine Whether a Decimal is a Solution of an Equation
In the following exercises, determine whether the each number is a solution of the given equation.
x−0.4=2.1
ⓐ x=1.7 ⓑ x=2.5
u2.5=−12.5
ⓐ u=−5ⓑ u=−31.25
Solve Equations with Decimals
In the following exercises, solve.
m+3.8=7.5
a+2.26=−1.1
x−0.24=−8.6
0.6p=13.2
−22.32=−2.4z
p−7=−4.2
Translate to an Equation and Solve
In the following exercises, translate and solve.
The difference of n and 15.2 is 4.4.
The quotient of y and −1.8 is −9.
Averages and Probability
Find the Mean of a Set of Numbers
In the following exercises, find the mean of the numbers.
2,4,1,0,1,and1
Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited 3,0,8,1,and8 minutes. Find the mean.
Find the Median of a Set of Numbers
In the following exercises, find the median.
41, 45, 32, 60, 58
The ages of the eight men in Jerry’s model train club are 52,63,45,51,55,75,60,and59. Find the median age.
The number of clients at Miranda’s beauty salon each weekday last week were 18,7,12,16,and20. Find the median number of clients.
Find the Mode of a Set of Numbers
In the following exercises, identify the mode of the numbers.
6, 4, 4,5, 6,6, 4, 4, 4, 3, 5
Use the Basic Definition of Probability
In the following exercises, solve. (Round decimals to three places.)
The Sustainability Club sells 200 tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.
Luc has to read 3 novels and 12 short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.
Ratios and Rate
Write a Ratio as a Fraction
In the following exercises, write each ratio as a fraction. Simplify the answer if possible.
28 to 40
3.5 to 0.5
134to158
64 ounces to 30 ounces
Write a Rate as a Fraction
In the following exercises, write each rate as a fraction. Simplify the answer if possible.
180 calories per 8 ounces
126 miles in 4 hours
Find Unit Rates
In the following exercises, find the unit rate.
180 calories per 8 ounces
126 miles in 4 hours
Find Unit Price
In the following exercises, find the unit price.
t-shirts: 3 for $8.97
An office supply store sells a box of pens for $11. The box contains 12 pens. How much does each pen cost?
Anna bought a pack of 8 kitchen towels for $13.20. How much did each towel cost? Round to the nearest cent if necessary.
In the following exercises, find each unit price and then determine the better buy.
Shampoo: 12 ounces for $4.29 or 22 ounces for $7.29?
Translate Phrases to Expressions with Fractions
In the following exercises, translate the English phrase into an algebraic expression.
535 miles per hhours
the ratio of 4y and the difference of x and 10
Simplify and Use Square Roots
Simplify Expressions with Square Roots
In the following exercises, simplify.
√64
−√25
√−9
√64+√225
Estimate Square Roots
In the following exercises, estimate each square root between two consecutive whole numbers.
√28
Approximate Square Roots
In the following exercises, approximate each square root and round to two decimal places.
√15
Simplify Variable Expressions with Square Roots
In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)
√q2
−√121a2
−√100q2
√4a2b2
Use Square Roots in Applications
In the following exercises, solve. Round to one decimal place.
Art Diego has 225 square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?
Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of 30 square feet. How long can a side of the flower garden be?
Gravity A hiker dropped a granola bar from a lookout spot 576 feet above a valley. How long did it take the granola bar to reach the valley floor?
Accident investigation The skid marks of a car involved in an accident were 216 feet. How fast had the car been going before applying the brakes?