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Prealgebra 2e

5.2 Decimal Operations

Prealgebra 2e5.2 Decimal Operations
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:

  • Add and subtract decimals
  • Multiply decimals
  • Divide decimals
  • Use decimals in money applications
Be Prepared 5.4

Before you get started, take this readiness quiz.

Simplify 70100.70100.
 If you missed this problem, review Example 4.19.

Be Prepared 5.5

Multiply 310·910.310·910.
 If you missed this problem, review Example 4.25.

Be Prepared 5.6

Divide −36÷(−9).−36÷(−9).
 If you missed this problem, review Example 3.49.

Add and Subtract Decimals

Let’s take one more look at the lunch order from the start of Decimals, this time noticing how the numbers were added together.

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

All three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal points lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimals this way, we can add or subtract the corresponding place values just as we did with whole numbers.

How To

Add or subtract decimals.

  1. Step 1. Write the numbers vertically so the decimal points line up.
  2. Step 2. Use zeros as place holders, as needed.
  3. Step 3. Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Example 5.11

Add: 3.7+12.4.3.7+12.4.

Try It 5.21

Add: 5.7+11.9.5.7+11.9.

Try It 5.22

Add: 18.32+14.79.18.32+14.79.

Example 5.12

Add: 23.5+41.38.23.5+41.38.

Try It 5.23

Add: 4.8+11.69.4.8+11.69.

Try It 5.24

Add: 5.123+18.47.5.123+18.47.

How much change would you get if you handed the cashier a $20$20 bill for a $14.65$14.65 purchase? We will show the steps to calculate this in the next example.

Example 5.13

Subtract: 20−14.65.20−14.65.

Try It 5.25

Subtract:

10−9.58.10−9.58.

Try It 5.26

Subtract:

50−37.42.50−37.42.

Example 5.14

Subtract: 2.51−7.4.2.51−7.4.

Try It 5.27

Subtract: 4.77−6.3.4.77−6.3.

Try It 5.28

Subtract: 8.12−11.7.8.12−11.7.

Multiply Decimals

Multiplying decimals is very much like multiplying whole numbers—we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first review multiplying fractions.

Do you remember how to multiply fractions? To multiply fractions, you multiply the numerators and then multiply the denominators.

So let’s see what we would get as the product of decimals by converting them to fractions first. We will do two examples side-by-side in Table 5.3. Look for a pattern.

A B
(0.3)(0.7)(0.3)(0.7) (0.2)(0.46)(0.2)(0.46)
Convert to fractions. (310)(710)(310)(710) (210)(46100)(210)(46100)
Multiply. 2110021100 921000921000
Convert back to decimals. 0.210.21 0.0920.092
Table 5.3

There is a pattern that we can use. In A, we multiplied two numbers that each had one decimal place, and the product had two decimal places. In B, we multiplied a number with one decimal place by a number with two decimal places, and the product had three decimal places.

How many decimal places would you expect for the product of (0.01)(0.004)?(0.01)(0.004)? If you said “five”, you recognized the pattern. When we multiply two numbers with decimals, we count all the decimal places in the factors—in this case two plus three—to get the number of decimal places in the product—in this case five.

The top line says 0.01 times 0.004 equals 0.00004. Below the 0.01, it says 2 places. Below the 0.004, it says 3 places. Below the 0.00004, it says 5 places. The bottom line says 1 over 100 times 4 over 1000 equals 4 over 100,000.

Once we know how to determine the number of digits after the decimal point, we can multiply decimal numbers without converting them to fractions first. The number of decimal places in the product is the sum of the number of decimal places in the factors.

The rules for multiplying positive and negative numbers apply to decimals, too, of course.

Multiplying Two Numbers

When multiplying two numbers,
  • if their signs are the same, the product is positive.
  • if their signs are different, the product is negative.

When you multiply signed decimals, first determine the sign of the product and then multiply as if the numbers were both positive. Finally, write the product with the appropriate sign.

How To

Multiply decimal numbers.

  1. Step 1. Determine the sign of the product.
  2. Step 2. Write the numbers in vertical format, lining up the numbers on the right.
  3. Step 3. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
  4. Step 4. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
  5. Step 5. Write the product with the appropriate sign.

Example 5.15

Multiply: (3.9)(4.075).(3.9)(4.075).

Try It 5.29

Multiply: 4.5(6.107).4.5(6.107).

Try It 5.30

Multiply: 10.79(8.12).10.79(8.12).

Example 5.16

Multiply: (−8.2)(5.19).(−8.2)(5.19).

Try It 5.31

Multiply: (4.63)(−2.9).(4.63)(−2.9).

Try It 5.32

Multiply: (−7.78)(4.9).(−7.78)(4.9).

In the next example, we’ll need to add several placeholder zeros to properly place the decimal point.

Example 5.17

Multiply: (0.03)(0.045).(0.03)(0.045).

Try It 5.33

Multiply: (0.04)(0.087).(0.04)(0.087).

Try It 5.34

Multiply: (0.09)(0.067).(0.09)(0.067).

Multiply by Powers of 1010

In many fields, especially in the sciences, it is common to multiply decimals by powers of 10.10. Let’s see what happens when we multiply 1.94361.9436 by some powers of 10.10.

The top row says 1.9436 times 10, then 1.9436 times 100, then 1.9436 times 1000. Below each is a vertical multiplication problem. These show that 1.9436 times 10 is 19.4360, 1.9436 times 100 is 194.3600, and 1.9436 times 1000 is 1943.6000.

Look at the results without the final zeros. Do you notice a pattern?

1.9436(10)=19.4361.9436(100)=194.361.9436(1000)=1943.61.9436(10)=19.4361.9436(100)=194.361.9436(1000)=1943.6

The number of places that the decimal point moved is the same as the number of zeros in the power of ten. Table 5.4 summarizes the results.

Multiply by Number of zeros Number of places decimal point moves
1010 11 11 place to the right
100100 22 22 places to the right
1,0001,000 33 33 places to the right
10,00010,000 44 44 places to the right
Table 5.4

We can use this pattern as a shortcut to multiply by powers of ten instead of multiplying using the vertical format. We can count the zeros in the power of 1010 and then move the decimal point that same of places to the right.

So, for example, to multiply 45.8645.86 by 100,100, move the decimal point 22 places to the right.

45.86 times 100 is shown to equal 4586. There is an arrow from the decimal going over 2 places from after the 5 to after the 6.

Sometimes when we need to move the decimal point, there are not enough decimal places. In that case, we use zeros as placeholders. For example, let’s multiply 2.42.4 by 100.100. We need to move the decimal point 22 places to the right. Since there is only one digit to the right of the decimal point, we must write a 00 in the hundredths place.

2.4 times 100 is shown to equal 240. There is an arrow from the decimal going over 2 places from after the 2 to after the 0.

How To

Multiply a decimal by a power of 10.

  1. Step 1. Move the decimal point to the right the same number of places as the number of zeros in the power of 10.10.
  2. Step 2. Write zeros at the end of the number as placeholders if needed.

Example 5.18

Multiply 5.635.63 by factors of ⓐ1010 ⓑ100100ⓒ1000.1000.

Try It 5.35

Multiply 2.582.58 by factors of ⓐ1010 ⓑ100100 ⓒ1000.1000.

Try It 5.36

Multiply 14.214.2 by factors of ⓐ1010 ⓑ100100 ⓒ1000.1000.

Divide Decimals

Just as with multiplication, division of decimals is very much like dividing whole numbers. We just have to figure out where the decimal point must be placed.

To understand decimal division, let’s consider the multiplication problem

(0.2)(4)=0.8(0.2)(4)=0.8

Remember, a multiplication problem can be rephrased as a division problem. So we can write

0.8÷4=0.20.8÷4=0.2

We can think of this as “If we divide 8 tenths into four groups, how many are in each group?” Figure 5.5 shows that there are four groups of two-tenths in eight-tenths. So 0.8÷4=0.2.0.8÷4=0.2.

A number line is shown with 0, 0.2, 0.4, 0.6, 0.8, and 1. There are braces showing a distance of 0.2 between each adjacent set of 2 numbers.
Figure 5.5

Using long division notation, we would write

A division problem is shown. 0.8 is on the inside of the division sign, 4 is on the outside. Above the division sign is 0.2.

Notice that the decimal point in the quotient is directly above the decimal point in the dividend.

To divide a decimal by a whole number, we place the decimal point in the quotient above the decimal point in the dividend and then divide as usual. Sometimes we need to use extra zeros at the end of the dividend to keep dividing until there is no remainder.

How To

Divide a decimal by a whole number.

  1. Step 1. Write as long division, placing the decimal point in the quotient above the decimal point in the dividend.
  2. Step 2. Divide as usual.

Example 5.19

Divide: 0.12÷3.0.12÷3.

Try It 5.37

Divide: 0.28÷4.0.28÷4.

Try It 5.38

Divide: 0.56÷7.0.56÷7.

In everyday life, we divide whole numbers into decimals—money—to find the price of one item. For example, suppose a case of 2424 water bottles cost $3.99.$3.99. To find the price per water bottle, we would divide $3.99$3.99 by 24,24, and round the answer to the nearest cent (hundredth).

Example 5.20

Divide: $3.99÷24.$3.99÷24.

Try It 5.39

Divide: $6.99÷36.$6.99÷36.

Try It 5.40

Divide: $4.99÷12.$4.99÷12.

Divide a Decimal by Another Decimal

So far, we have divided a decimal by a whole number. What happens when we divide a decimal by another decimal? Let’s look at the same multiplication problem we looked at earlier, but in a different way.

(0.2)(4)=0.8(0.2)(4)=0.8

Remember, again, that a multiplication problem can be rephrased as a division problem. This time we ask, “How many times does 0.20.2 go into 0.8?”0.8?” Because (0.2)(4)=0.8,(0.2)(4)=0.8, we can say that 0.20.2 goes into 0.80.8 four times. This means that 0.80.8 divided by 0.20.2 is 4.4.

0.8÷0.2=40.8÷0.2=4
A number line is shown with 0, 0.2, 0.4, 0.6, 0.8, and 1. There are braces showing a distance of 0.2 between each adjacent set of 2 numbers.

We would get the same answer, 4,4, if we divide 88 by 2,2, both whole numbers. Why is this so? Let’s think about the division problem as a fraction.

0.80.2(0.8)10(0.2)108240.80.2(0.8)10(0.2)10824

We multiplied the numerator and denominator by 1010 and ended up just dividing 88 by 2.2. To divide decimals, we multiply both the numerator and denominator by the same power of 1010 to make the denominator a whole number. Because of the Equivalent Fractions Property, we haven’t changed the value of the fraction. The effect is to move the decimal points in the numerator and denominator the same number of places to the right.

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

It may help to review the vocabulary for division:

a divided by b is shown with a labeled as the dividend and b labeled as the divisor. Then a over b is shown with a labeled as the divided and b labeled as the divisor. Then a is shown inside a division problem with b on the outside with a labeled as the dividend and b labeled as the divisor.

How To

Divide decimal numbers.

  1. Step 1. Determine the sign of the quotient.
  2. Step 2. Make the divisor a whole number by moving the decimal point all the way to the right. Move the decimal point in the dividend the same number of places to the right, writing zeros as needed.
  3. Step 3. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
  4. Step 4. Write the quotient with the appropriate sign.

Example 5.21

Divide: −2.89÷(3.4).−2.89÷(3.4).

Try It 5.41

Divide: −1.989÷5.1.−1.989÷5.1.

Try It 5.42

Divide: −2.04÷5.1.−2.04÷5.1.

Example 5.22

Divide: −25.65÷(−0.06).−25.65÷(−0.06).

Try It 5.43

Divide: −23.492÷(−0.04).−23.492÷(−0.04).

Try It 5.44

Divide: −4.11÷(−0.12).−4.11÷(−0.12).

Now we will divide a whole number by a decimal number.

Example 5.23

Divide: 4÷0.05.4÷0.05.

Try It 5.45

Divide: 6÷0.03.6÷0.03.

Try It 5.46

Divide: 7÷0.02.7÷0.02.

Use Decimals in Money Applications

We often apply decimals in real life, and most of the applications involving money. The Strategy for Applications we used in The Language of Algebra gives us a plan to follow to help find the answer. Take a moment to review that strategy now.

Strategy for Applications

  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Answer the question with a complete sentence.

Example 5.24

Paul received $50$50 for his birthday. He spent $31.64$31.64 on a video game. How much of Paul’s birthday money was left?

Try It 5.47

Nicole earned $35$35 for babysitting her cousins, then went to the bookstore and spent $18.48$18.48 on books and coffee. How much of her babysitting money was left?

Try It 5.48

Amber bought a pair of shoes for $24.75$24.75 and a purse for $36.90.$36.90. The sales tax was $4.32.$4.32. How much did Amber spend?

Example 5.25

Jessie put 88 gallons of gas in her car. One gallon of gas costs $3.529.$3.529. How much does Jessie owe for the gas? (Round the answer to the nearest cent.)

Try It 5.49

Hector put 1313 gallons of gas into his car. One gallon of gas costs $3.175.$3.175. How much did Hector owe for the gas? Round to the nearest cent.

Try It 5.50

Christopher bought 55 pizzas for the team. Each pizza cost $9.75.$9.75. How much did all the pizzas cost?

Example 5.26

Four friends went out for dinner. They shared a large pizza and a pitcher of soda. The total cost of their dinner was $31.76.$31.76. If they divide the cost equally, how much should each friend pay?

Try It 5.51

Six friends went out for dinner. The total cost of their dinner was $92.82.$92.82. If they divide the bill equally, how much should each friend pay?

Try It 5.52

Chad worked 4040 hours last week and his paycheck was $570.$570. How much does he earn per hour?

Be careful to follow the order of operations in the next example. Remember to multiply before you add.

Example 5.27

Marla buys 66 bananas that cost $0.22$0.22 each and 44 oranges that cost $0.49$0.49 each. How much is the total cost of the fruit?

Try It 5.53

Suzanne buys 33 cans of beans that cost $0.75$0.75 each and 66 cans of corn that cost $0.62$0.62 each. How much is the total cost of these groceries?

Try It 5.54

Lydia bought movie tickets for the family. She bought two adult tickets for $9.50$9.50 each and four children’s tickets for $6.00$6.00 each. How much did the tickets cost Lydia in all?

Section 5.2 Exercises

Practice Makes Perfect

Add and Subtract Decimals

In the following exercises, add or subtract.

95.

16.92+7.5616.92+7.56

96.

18.37+9.3618.37+9.36

97.

256.37−85.49256.37−85.49

98.

248.25−91.29248.25−91.29

99.

21.76−30.9921.76−30.99

100.

15.35−20.8815.35−20.88

101.

37.5+12.2337.5+12.23

102.

38.6+13.6738.6+13.67

103.

−16.53−24.38−16.53−24.38

104.

−19.47−32.58−19.47−32.58

105.

−38.69+31.47−38.69+31.47

106.

−29.83+19.76−29.83+19.76

107.

−4.2+(−9.3)−4.2+(−9.3)

108.

−8.6+(−8.6)−8.6+(−8.6)

109.

100−64.2100−64.2

110.

100−65.83100−65.83

111.

72.5−10072.5−100

112.

86.2−10086.2−100

113.

15+0.7315+0.73

114.

27+0.8727+0.87

115.

2.51+402.51+40

116.

9.38+609.38+60

117.

91.75−(−10.462)91.75−(−10.462)

118.

94.69−(−12.678)94.69−(−12.678)

119.

55.01−3.755.01−3.7

120.

59.08−4.659.08−4.6

121.

2.51−7.42.51−7.4

122.

3.84−6.13.84−6.1

Multiply Decimals

In the following exercises, multiply.

123.

(0.3)(0.4)(0.3)(0.4)

124.

(0.6)(0.7)(0.6)(0.7)

125.

(0.24)(0.6)(0.24)(0.6)

126.

(0.81)(0.3)(0.81)(0.3)

127.

(5.9)(7.12)(5.9)(7.12)

128.

(2.3)(9.41)(2.3)(9.41)

129.

(8.52)(3.14)(8.52)(3.14)

130.

(5.32)(4.86)(5.32)(4.86)

131.

(−4.3)(2.71)(−4.3)(2.71)

132.

(−8.5)(1.69)(−8.5)(1.69)

133.

(−5.18)(−65.23)(−5.18)(−65.23)

134.

(−9.16)(−68.34)(−9.16)(−68.34)

135.

(0.09)(24.78)(0.09)(24.78)

136.

(0.04)(36.89)(0.04)(36.89)

137.

(0.06)(21.75)(0.06)(21.75)

138.

(0.08)(52.45)(0.08)(52.45)

139.

(9.24)(10)(9.24)(10)

140.

(6.531)(10)(6.531)(10)

141.

(55.2)(1,000)(55.2)(1,000)

142.

(99.4)(1,000)(99.4)(1,000)

Divide Decimals

In the following exercises, divide.

143.

0.15÷50.15÷5

144.

0.27÷30.27÷3

145.

4.75÷254.75÷25

146.

12.04÷4312.04÷43

147.

$8.49÷12$8.49÷12

148.

$16.99÷9$16.99÷9

149.

$117.25÷48$117.25÷48

150.

$109.24÷36$109.24÷36

151.

0.6÷0.20.6÷0.2

152.

0.8÷0.40.8÷0.4

153.

1.44÷(−0.3)1.44÷(−0.3)

154.

1.25÷(−0.5)1.25÷(−0.5)

155.

−1.75÷(−0.05)−1.75÷(−0.05)

156.

−1.15÷(−0.05)−1.15÷(−0.05)

157.

5.2÷2.55.2÷2.5

158.

6.5÷3.256.5÷3.25

159.

12÷0.0812÷0.08

160.

5÷0.045÷0.04

161.

11÷0.5511÷0.55

162.

14÷0.3514÷0.35

Mixed Practice

In the following exercises, simplify.

163.

6(12.4−9.2)6(12.4−9.2)

164.

3(15.7−8.6)3(15.7−8.6)

165.

24(0.5)+(0.3)224(0.5)+(0.3)2

166.

35(0.2)+(0.9)235(0.2)+(0.9)2

167.

1.15(26.83+1.61)1.15(26.83+1.61)

168.

1.18(46.22+3.71)1.18(46.22+3.71)

169.

$45+0.08($45)$45+0.08($45)

170.

$63+0.18($63)$63+0.18($63)

171.

18÷(0.75+0.15)18÷(0.75+0.15)

172.

27÷(0.55+0.35)27÷(0.55+0.35)

173.

(1.43+0.27)÷(0.9−0.05)(1.43+0.27)÷(0.9−0.05)

174.

(1.5−0.06)÷(0.12+0.24)(1.5−0.06)÷(0.12+0.24)

175.

[$75.42+0.18($75.42)]÷5[$75.42+0.18($75.42)]÷5

176.

[$56.31+0.22($56.31)]÷4[$56.31+0.22($56.31)]÷4

Use Decimals in Money Applications

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

177.

Spending money Brenda got $40$40 from the ATM. She spent $15.11$15.11 on a pair of earrings. How much money did she have left?

178.

Spending money Marissa found $20$20 in her pocket. She spent $4.82$4.82 on a smoothie. How much of the $20$20 did she have left?

179.

Shopping Adam bought a t-shirt for $18.49$18.49 and a book for $8.92$8.92 The sales tax was $1.65.$1.65. How much did Adam spend?

180.

Restaurant Roberto’s restaurant bill was $20.45$20.45 for the entrée and $3.15$3.15 for the drink. He left a $4.40$4.40 tip. How much did Roberto spend?

181.

Coupon Emily bought a box of cereal that cost $4.29.$4.29. She had a coupon for $0.55$0.55 off, and the store doubled the coupon. How much did she pay for the box of cereal?

182.

Coupon Diana bought a can of coffee that cost $7.99.$7.99. She had a coupon for $0.75$0.75 off, and the store doubled the coupon. How much did she pay for the can of coffee?

183.

Diet Leo took part in a diet program. He weighed 190190 pounds at the start of the program. During the first week, he lost 4.34.3 pounds. During the second week, he had lost 2.82.8 pounds. The third week, he gained 0.70.7 pounds. The fourth week, he lost 1.91.9 pounds. What did Leo weigh at the end of the fourth week?

184.

Snowpack On April 1,1, the snowpack at the ski resort was 44 meters deep, but the next few days were very warm. By April 5,5, the snow depth was 1.61.6 meters less. On April 8,8, it snowed and added 2.12.1 meters of snow. What was the total depth of the snow?

185.

Coffee Noriko bought 44 coffees for herself and her co-workers. Each coffee was $3.75.$3.75. How much did she pay for all the coffees?

186.

Subway Fare Arianna spends $4.50$4.50 per day on subway fare. Last week she rode the subway 66 days. How much did she spend for the subway fares?

187.

Income Mayra earns $9.25$9.25 per hour. Last week she worked 3232 hours. How much did she earn?

188.

Income Peter earns $8.75$8.75 per hour. Last week he worked 1919 hours. How much did he earn?

189.

Hourly Wage Alan got his first paycheck from his new job. He worked 3030 hours and earned $382.50.$382.50. How much does he earn per hour?

190.

Hourly Wage Maria got her first paycheck from her new job. She worked 2525 hours and earned $362.50.$362.50. How much does she earn per hour?

191.

Restaurant Jeannette and her friends love to order mud pie at their favorite restaurant. They always share just one piece of pie among themselves. With tax and tip, the total cost is $6.00.$6.00. How much does each girl pay if the total number sharing the mud pie is

ⓐ 2?2?

ⓑ 3?3?

ⓒ 4?4?

ⓓ 5?5?

ⓔ 6?6?

192.

Pizza Alex and his friends go out for pizza and video games once a week. They share the cost of a $15.60$15.60 pizza equally. How much does each person pay if the total number sharing the pizza is

ⓐ 2?2?

ⓑ 3?3?

ⓒ 4?4?

ⓓ 5?5?

ⓔ 6?6?

193.

Fast Food At their favorite fast food restaurant, the Carlson family orders 44 burgers that cost $3.29$3.29 each and 22 orders of fries at $2.74$2.74 each. What is the total cost of the order?

194.

Home Goods Chelsea needs towels to take with her to college. She buys 22 bath towels that cost $9.99$9.99 each and 66 washcloths that cost $2.99$2.99 each. What is the total cost for the bath towels and washcloths?

195.

Zoo The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost $29.95$29.95 and children’s tickets cost $19.95.$19.95. What will the total cost be for 44 adults and 77 children?

196.

Ice Skating Jasmine wants to have her birthday party at the local ice skating rink. It will cost $8.25$8.25 per child and $12.95$12.95 per adult. What will the total cost be for 1212 children and 33 adults?

Everyday Math

197.

Paycheck Annie has two jobs. She gets paid $14.04$14.04 per hour for tutoring at City College and $8.75$8.75 per hour at a coffee shop. Last week she tutored for 88 hours and worked at the coffee shop for 1515 hours.

ⓐ How much did she earn?

ⓑ If she had worked all 2323 hours as a tutor instead of working both jobs, how much more would she have earned?

198.

Paycheck Jake has two jobs. He gets paid $7.95$7.95 per hour at the college cafeteria and $20.25$20.25 at the art gallery. Last week he worked 1212 hours at the cafeteria and 55 hours at the art gallery.

ⓐ How much did he earn?

ⓑ If he had worked all 1717 hours at the art gallery instead of working both jobs, how much more would he have earned?

Writing Exercises

199.

At the 2010 winter Olympics, two skiers took the silver and bronze medals in the Men's Super-G ski event. Miller's time was 11 minute 30.6230.62 seconds and Weibrecht's time was 11 minute 30.6530.65 seconds. Find the difference in their times and then write the name of that decimal.

200.

Find the quotient of 0.12÷0.040.12÷0.04 and explain in words all the steps taken.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

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