Review Exercises

Decimals
Name Decimals

In the following exercises, name each decimal.

  1. 0.8
  2. 0.375
  3. 0.007
  4. 5.24
  5. −12.5632
  6. −4.09
    Write Decimals

In the following exercises, write as a decimal.

  1. three tenths
  2. nine hundredths
  3. twenty-seven hundredths
  4. ten and thirty-five thousandths
  5. negative twenty and three tenths
  6. negative five hundredths
    Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

  1. 0.43
  2. 0.825
  3. 9.7
  4. 3.64
    Locate Decimals on the Number Line
  5. ⓐ0.6
    ⓑ−0.9

ⓒ2.2

ⓓ−1.3

Order Decimals

In the following exercises, order each of the following pairs of numbers, using < or >.

  1. 0.6___0.8
  2. 0.2___0.15
  3. 0.803____0.83
  4. −0.56____−0.562
    Round Decimals

In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number.

  1. 12.529
  2. 4.8447
  3. 5.897
    Decimal Operations
    Add and Subtract Decimals

In the following exercises, add or subtract.

  1. 5.75+8.46
  2. 32.89−8.22
  3. 24−19.31
  4. 10.2+14.631
  5. −6.4+(−2.9)
  6. 1.83−4.2
    Multiply Decimals

In the following exercises, multiply.

  1. (0.3)(0.7)
  2. (−6.4)(0.25)
  3. (−3.35)(−12.7)
  4. (15.4)(1000)
    Divide Decimals

In the following exercises, divide.

  1. 0.48÷6
  2. 4.32÷24
  3. $6.29÷12
  4. (−0.8)÷(−0.2)
  5. 1.65÷0.15
  6. 9÷0.045
    Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

  1. 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.
  2. 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?
  3. A pack of 16 water bottles cost $6.72. How much did each bottle cost?
  4. 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.

  1. 35
  2. 78
  3. −1920
  4. −214
  5. 13
  6. 611
    Order Decimals and Fractions

In the following exercises, order each pair of numbers, using < or >.

  1. 12___0.2
  2. 35___0.
  3. −78___−0.84
  4. −512___−0.42
  5. 0.625___1320
  6. 0.33___516
    In the following exercises, write each set of numbers in order from least to greatest.
  7. 23,1720,0.65
  8. 79,0.75,1115
    Simplify Expressions Using the Order of Operations

In the following exercises, simplify

  1. 4(10.3−5.8)
  2. 34(15.44−7.4)
  3. 30÷(0.45+0.15)
  4. 1.6+38
  5. 52(0.5)+(0.4)2
  6. −25⋅910+0.14
    Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.

  1. radius=6 in.
  2. radius=3.5 ft.
  3. radius=733m
  4. diameter=11 cm
    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.

  1. x−0.4=2.1
    ⓐx=1.7 ⓑx=2.5
  2. y+3.2=−1.5
    ⓐy=1.7ⓑy=−4.7
  3. u2.5=−12.5
    ⓐu=−5ⓑu=−31.25
  4. 0.45v=−40.5
    ⓐv=−18.225ⓑv=−90
    Solve Equations with Decimals

In the following exercises, solve.

  1. m+3.8=7.5
  2. h+5.91=2.4
  3. a+2.26=−1.1
  4. p−4.3=−1.65
  5. x−0.24=−8.6
  6. j−7.42=−3.7
  7. 0.6p=13.2
  8. −8.6x=34.4
  9. −22.32=−2.4z
  10. a0.3=−24
  11. p−7=−4.2
  12. s−2.5=−10
    Translate to an Equation and Solve

In the following exercises, translate and solve.

  1. The difference of n and 15.2 is 4.4.
  2. The product of −5.9 and x is −3.54.
  3. The quotient of y and −1.8 is −9.
  4. The sum of m and (−4.03) is 6.8.
    Averages and Probability
    Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

  1. 2,4,1,0,1,and1
  2. $270, $310.50, $243.75, and$252.15
  3. 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.
  4. In the last three months, Raul’s water bills were $31.45,$48.76,and$42.60. Find the mean.
    Find the Median of a Set of Numbers

In the following exercises, find the median.

  1. 41, 45, 32, 60, 58
  2. 25, 23, 24, 26, 29, 19, 18, 32
  3. 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.
  4. 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.

  1. 6, 4, 4,5, 6,6, 4, 4, 4, 3, 5
  2. The number of siblings of a group of students: 2, 0, 3, 2, 4, 1, 6, 5, 4, 1, 2, 3
    Use the Basic Definition of Probability

In the following exercises, solve. (Round decimals to three places.)

  1. 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.
  2. 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.

  1. 28 to 40
  2. 56 to 32
  3. 3.5 to 0.5
  4. 1.2 to 1.8
  5. 134to158
  6. 213to514
  7. 64 ounces to 30 ounces
  8. 28 inches to 3 feet
    Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

  1. 180 calories per 8 ounces
  2. 90 pounds per 7.5 square inches
  3. 126 miles in 4 hours
  4. $612.50 for 35 hours
    Find Unit Rates

In the following exercises, find the unit rate.

  1. 180 calories per 8 ounces
  2. 90 pounds per 7.5 square inches
  3. 126 miles in 4 hours
  4. $612.50 for 35 hours
    Find Unit Price

In the following exercises, find the unit price.

In the following exercises, translate the English phrase into an algebraic expression.

  1. t-shirts: 3 for $8.97
  2. Highlighters: 6 for $2.52
  3. An office supply store sells a box of pens for $11. The box contains 12 pens. How much does each pen cost?
  4. 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.
  5. Shampoo: 12 ounces for $4.29 or 22 ounces for $7.29?
  6. Vitamins: 60 tablets for $6.49 or 100 for $11.99?
    Translate Phrases to Expressions with Fractions
  1. 535 miles per hhours
  2. a adults to 45 children
  3. the ratio of 4y and the difference of x and 10
  4. the ratio of 19 and the sum of 3 and n
    Simplify and Use Square Roots
    Simplify Expressions with Square Roots

In the following exercises, simplify.