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Add Integers

3.2 Add Integers

Learning Objectives

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

  • Model addition of integers
  • Simplify expressions with integers
  • Evaluate variable expressions with integers
  • Translate word phrases to algebraic expressions
  • Add integers in applications

Be Prepared 3.3

Before you get started, take this readiness quiz.

Evaluate x+8x+8 when x=6.x=6.
 If you missed this problem, review Example 2.13.

Simplify: 8+2(5+1).8+2(5+1).
 If you missed this problem, review Example 2.8.

Translate the sum of 33 and negative 77 into an algebraic expression.
 If you missed this problem, review Table 2.7

Model Addition of Integers

Now that we have located positive and negative numbers on the number line, it is time to discuss arithmetic operations with integers.

Most students are comfortable with the addition and subtraction facts for positive numbers. But doing addition or subtraction with both positive and negative numbers may be more difficult. This difficulty relates to the way the brain learns.

The brain learns best by working with objects in the real world and then generalizing to abstract concepts. Toddlers learn quickly that if they have two cookies and their older brother steals one, they have only one left. This is a concrete example of 2−1.2−1. Children learn their basic addition and subtraction facts from experiences in their everyday lives. Eventually, they know the number facts without relying on cookies.

Addition and subtraction of negative numbers have fewer real world examples that are meaningful to us. Math teachers have several different approaches, such as number lines, banking, temperatures, and so on, to make these concepts real.

We will model addition and subtraction of negatives with two color counters. We let a blue counter represent a positive and a red counter will represent a negative.

This figure has a blue circle labeled positive and a red circle labeled negative.

If we have one positive and one negative counter, the value of the pair is zero. They form a neutral pair. The value of this neutral pair is zero as summarized in Figure 3.17.

This figure has a blue circle over a red circle. Beside them is the statement 1 plus negative 1 equals 0.
Figure 3.17 A blue counter represents +1.+1. A red counter represents −1.−1. Together they add to zero.

Manipulative Mathematics

Doing the Manipulative Mathematics activity "Addition of signed Numbers" will help you develop a better understanding of adding integers.

We will model four addition facts using the numbers 5,−5and3,−3.5,−5and3,−3.

5+3−5+(−3)−5+35+(−3)5+3−5+(−3)−5+35+(−3)

Example 3.14

Model: 5+3.5+3.

Solution

Interpret the expression. 5+35+3 means the sum of 55 and 33.
Model the first number. Start with 5 positives. Five light blue circles are horizontally aligned, with the number '5' positioned directly beneath the central circle, representing the total count of the circles shown.
Model the second number. Add 3 positives. Two groups of light blue circles are shown against a white background. The first group contains five circles, with the number '5' written below them. The second group consists of three circles, with the number '3' below.
Count the total number of counters. Eight light blue circles, arranged in a row, with the text '8 positives' written directly below them, illustrating a concept likely related to mathematics or data representation.
The sum of 5 and 3 is 8. 5+3=85+3=8

Try It 3.27

Model the expression.

2+42+4

Try It 3.28

Model the expression.

2+52+5

Example 3.15

Model: −5+(−3).−5+(−3).

Solution

Interpret the expression. −5+(−3)−5+(−3) means the sum of −5−5 and −3−3.
Model the first number. Start with 5 negatives. Five light red circles are arranged horizontally on a white background, with the number '-5' centered beneath them.
Model the second number. Add 3 negatives. Five red circles are grouped together representing -5, while three red circles are grouped separately representing -3 on a white background.
Count the total number of counters. Eight light red circles with red outlines are arranged in a row. Below them, the text '8 negatives' is written in dark blue, indicating they represent negative values.
The sum of −5 and −3 is −8. −5+−3=−8−5+−3=−8

Try It 3.29

Model the expression.

−2+(−4)−2+(−4)

Try It 3.30

Model the expression.

−2+(−5)−2+(−5)

Example 3.14 and Example 3.15 are very similar. The first example adds 55 positives and 33 positives—both positives. The second example adds 55 negatives and 33 negatives—both negatives. In each case, we got a result of 8—either88—either8 positives or 88 negatives. When the signs are the same, the counters are all the same color.

Now let’s see what happens when the signs are different.

Example 3.16

Model: −5+3.−5+3.

Solution

Interpret the expression. −5+3−5+3 means the sum of −5−5 and 33.
Model the first number. Start with 5 negatives. Five light red circles, uniformly spaced, are arranged in a horizontal line against a plain white background.
Model the second number. Add 3 positives. Five red circles are arranged in a horizontal row above three light blue circles, also in a horizontal row, set against a plain white background.
Remove any neutral pairs. Three magenta ovals, each containing a red and a blue circle, are shown alongside two separate red circles.
Count the result. A diagram displays two red-outlined pink circles, side-by-side, with the label '2 negatives' written below them on a white background, representing negative values or concepts.
The sum of −5 and 3 is −2. −5+3=−2−5+3=−2

Notice that there were more negatives than positives, so the result is negative.

Try It 3.31

Model the expression, and then simplify:

2+(−4)2+(−4)

Try It 3.32

Model the expression, and then simplify:

2+(−5)2+(−5)

Example 3.17

Model: 5+(−3).5+(−3).

Solution

Interpret the expression. 5+(−3)5+(−3) means the sum of 55 and −3−3.
Model the first number. Start with 5 positives. Five light blue circles with a darker blue outline are arranged in a horizontal line on a white background, resembling a star rating system or a progress indicator.
Model the second number. Add 3 negatives. An illustration showing five light blue circles in the top row and three red circles in the bottom row.
Remove any neutral pairs. Three pairs of light blue and red circles are grouped within magenta ovals, followed by two standalone light blue circles, illustrating a mix of grouped and individual elements.
Count the result. Two light blue circles are displayed above the text '2 positives' on a white background, indicating a count of two positive results or items.
The sum of 5 and −3 is 2. 5+(−3)=25+(−3)=2

Try It 3.33

Model the expression, and then simplify:

(−2)+4(−2)+4

Try It 3.34

Model the expression:

(−2)+5(−2)+5

Example 3.18

Modeling Addition of Positive and Negative Integers

Model each addition.

  1. ⓐ 4 + 2
  2. ⓑ −3 + 6
  3. ⓒ 4 + (−5)
  4. ⓓ -2 + (−3)

Solution

ⓐ
4+24+2
Start with 4 positives. Four light blue circles with blue outlines are arranged horizontally on a white background, suggesting a selection or progress indicator.
Add two positives. Six light blue circles with blue outlines are arranged in a horizontal row, separated into a group of four and a group of two, on a white background.
How many do you have? 4+2=64+2=6
This table illustrates the addition problem 4 + 2, detailing each step with a description and its corresponding mathematical or visual representation.
ⓑ
−3+6−3+6
Start with 3 negatives. Three light red circles with dark red outlines are arranged horizontally on a white background.
Add 6 positives. An image displaying three red circles in the top row and six blue circles in the bottom row, representing a 3:6 ratio or comparison.
Remove neutral pairs. An array of circles: 3 red and 3 blue circles encircled by an arrowed loop, suggesting repetition. This is followed by 3 more blue circles and an ellipsis indicating continuation.
How many are left? Three light blue circles with a blue outline, arranged horizontally on a white background.
33. −3+6=3−3+6=3
Visual step-by-step demonstration of integer addition for -3 + 6, showing the process and result.
ⓒ
4+(−5)4+(−5)
Start with 4 positives. Four light blue circles, outlined in a slightly darker blue, are arranged horizontally on a white background.
Add 5 negatives. Two rows of circles are displayed on a white background: four light blue circles are in the top row, and five red circles are in the bottom row.
Remove neutral pairs. Eight circles, four blue and four red, are grouped by an oval, while one red circle is separate.
How many are left? A single, plain light pink or pale red circle with a darker red outline is centered against a pristine white background. The simple, minimalist design highlights the single geometric shape.
−1−1. 4+(−5)=−14+(−5)=−1
Visual demonstration of adding 4 and -5, resulting in -1, using a step-by-step approach with illustrations.
ⓓ
−2+(−3)−2+(−3)
Start with 2 negatives. Two light red circles with thin dark red outlines and subtle shadows are positioned horizontally close to each other on a plain white background, appearing as simple graphic elements.
Add 3 negatives. A simple graphic featuring two light red circles on the left, separated by space from three light red circles on the right, all against a white background.
How many do you have? −5−5. −2+(−3)=−5−2+(−3)=−5
Step-by-step demonstration of adding negative integers (-2 + -3 = -5) using descriptions, math, and visuals.

Try It 3.35

Model each addition.

  1. ⓐ 3 + 4
  2. ⓑ −1 + 4
  3. ⓒ 4 + (−6)
  4. ⓓ −2 + (−2)

Try It 3.36

  1. ⓐ 5 + 1
  2. ⓑ −3 + 7
  3. ⓒ 2 + (−8)
  4. ⓓ −3 + (−4)

Simplify Expressions with Integers

Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions with any integers.

For example, if you want to add 37+(−53),37+(−53), you don’t have to count out 3737 blue counters and 5353 red counters.

Picture 3737 blue counters with 5353 red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because 53−37=16,53−37=16, there are 1616 more negative counters.

37+(−53)=−1637+(−53)=−16

Let’s try another one. We’ll add −74+(−27).−74+(−27). Imagine 7474 red counters and 2727 more red counters, so we have 101101 red counters all together. This means the sum is −101.−101.

−74+(−27)=−101−74+(−27)=−101

Look again at the results of Example 3.14 - Example 3.17.

5+35+3 −5+(−3)−5+(−3)
both positive, sum positive both negative, sum negative
When the signs are the same, the counters would be all the same color, so add them.
−5+3−5+3 5+(−3)5+(−3)
different signs, more negatives different signs, more positives
Sum negative sum positive
When the signs are different, some counters would make neutral pairs; subtract to see how many are left.
Table 3.1 Addition of Positive and Negative Integers

Example 3.19

Simplify:

  1. ⓐ 19+(−47)19+(−47)
  2. ⓑ −32+40−32+40

Solution

ⓐ Since the signs are different, we subtract 1919 from 47.47. The answer will be negative because there are more negatives than positives.

19 + ( −47 ) −28 19 + ( −47 ) −28

ⓑ The signs are different so we subtract 3232 from 40.40. The answer will be positive because there are more positives than negatives

−32 + 40 8 −32 + 40 8

Try It 3.37

Simplify each expression:

  1. ⓐ 15+(−32)15+(−32)
  2. ⓑ −19+76−19+76

Try It 3.38

Simplify each expression:

  1. ⓐ −55+9−55+9
  2. ⓑ 43+(−17)43+(−17)

Example 3.20

Simplify: −14+(−36).−14+(−36).

Solution

Since the signs are the same, we add. The answer will be negative because there are only negatives.

−14 + ( −36 ) −50 −14 + ( −36 ) −50

Try It 3.39

Simplify the expression:

−31+(−19)−31+(−19)

Try It 3.40

Simplify the expression:

−42+(−28)−42+(−28)

The techniques we have used up to now extend to more complicated expressions. Remember to follow the order of operations.

Example 3.21

Simplify: −5+3(−2+7).−5+3(−2+7).

Solution

−5+3(−2+7)−5+3(−2+7)
Simplify inside the parentheses. −5+3(5)−5+3(5)
Multiply. −5+15−5+15
Add left to right. 1010
This table illustrates the step-by-step simplification of the mathematical expression -5 + 3(-2 + 7) following the order of operations.

Try It 3.41

Simplify the expression:

−2+5(−4+7)−2+5(−4+7)

Try It 3.42

Simplify the expression:

−4+2(−3+5)−4+2(−3+5)

Evaluate Variable Expressions with Integers

Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions.

Example 3.22

Evaluate x+7whenx+7when

  1. ⓐ x=−2x=−2
  2. ⓑ x=−11.x=−11.

Solution

ⓐ Evaluate x+7x+7 when x=−2x=−2
A mathematical expression showing '-2 + 7'. The number -2 is in red, while the addition sign and the number 7 are in black.
The image shows the text 'Substitute -2 for x.' with '-2' highlighted in red, indicating a mathematical instruction to replace the variable x with the value -2. A mathematical expression showing '-2 + 7'. The number -2 is in red, while the addition sign and the number 7 are in black.
Simplify. The number 5, written in black, appears in the top right corner of a plain white background.
ⓑ Evaluate x+7x+7 when x=−11x=−11
The image displays the mathematical expression 'x + 7' in a clear, sans-serif font against a white background.
The image shows the mathematical instruction, 'Substitute -11 for x.' The number -11 is highlighted in red, indicating its importance in the substitution. The image displays a mathematical expression showing the sum of negative eleven and positive seven, written as -11 + 7, with the negative number in red and the positive number and plus sign in black.
Simplify. A close-up view shows the number '-4' in black text against a plain white background.

Try It 3.43

Evaluate each expression for the given values:

x+5whenx+5when

  1. ⓐ x=−3andx=−3and
  2. ⓑ x=−17x=−17

Try It 3.44

Evaluate each expression for the given values: y+7y+7 when

  1. ⓐ y=−5y=−5
  2. ⓑ y=−8y=−8

Example 3.23

When n=−5,n=−5, evaluate

  1. ⓐ n+1n+1
  2. ⓑ −n+1.−n+1.

Solution

ⓐ Evaluate n+1n+1 when n=−5n=−5
The mathematical expression 'n + 1' is shown in a black, bold font on a white background.
The text 'Substitute -5 for n.' is displayed, instructing the viewer to replace the variable 'n' with the value -5. The image displays the mathematical expression '-5 + 1' with the number -5 in red and +1 in black, representing an arithmetic problem involving integers.
Simplify. The number negative four, or -4, displayed prominently on a white background.
ⓑ Evaluate −n+1−n+1 when n=−5n=−5
The mathematical expression -n + 1 is displayed in a clear, bold font against a white background.
The text reads 'Substitute -5 for n.' with '-5' highlighted in red, indicating a specific instruction for a mathematical or variable substitution. A mathematical expression shows the operation minus, followed by an opening parenthesis, then minus five, a closing parenthesis, then plus one. The number '5' and the minus sign before it are in red.
Simplify. The image displays a simple mathematical expression '5+1' in black text against a white background, representing an addition problem.
Add. A stark white image with a barely discernible '6' in the top right corner.

Try It 3.45

When n=−8,n=−8, evaluate

  1. ⓐ n+2n+2
  2. ⓑ −n+2−n+2

Try It 3.46

Wheny=−9,evaluateWheny=−9,evaluate

  1. ⓐ y+8y+8
  2. ⓑ −y+8.−y+8.

Next we'll evaluate an expression with two variables.

Example 3.24

Evaluate 3a+b3a+b when a=12a=12 and b=−30.b=−30.

Solution

The mathematical expression '3a + b' is shown against a white background.
The text 'Substitute 12 for a and -30 for b.' is displayed on a white background, with '12' in red and '-30' in light blue, and the rest of the text in dark gray. The mathematical expression 3(12) + (-30) is displayed, with the number 12 highlighted in red and -30 highlighted in blue.
Multiply. The image displays the mathematical expression '36 + (-30)' in black text against a white background.
Add. A plain white background featuring the number '6' subtly positioned in the top right corner.

Try It 3.47

Evaluate the expression:

a+2bwhena=−19andb=14.a+2bwhena=−19andb=14.

Try It 3.48

Evaluate the expression:

5p+qwhenp=4andq=−7.5p+qwhenp=4andq=−7.

Example 3.25

Evaluate (x+y)2(x+y)2 when x=−18x=−18 and y=24.y=24.

Solution

This expression has two variables. Substitute −18−18 for xx and 2424 for y.y.

(x+y)2(x+y)2
The text reads: 'Substitute -18 for x and 24 for y.' The number -18 is highlighted in red, and 24 is highlighted in light blue. (−18+24)2(−18+24)2
Add inside the parentheses. (6)2(6)2
Simplify 3636

Try It 3.49

Evaluate:

(x+y)2(x+y)2 when x=−15x=−15 and y=29.y=29.

Try It 3.50

Evaluate:

(x+y)3(x+y)3 when x=−8x=−8 and y=10.y=10.

Translate Word Phrases to Algebraic Expressions

All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase the sum indicates addition.

Example 3.26

Translate and simplify: the sum of −9−9 and 5.5.

Solution

The sum of −9 and 5 indicates addition. the sum of −9−9 and 55
Translate. −9+5−9+5
Simplify. −4−4
Steps to translate a verbal mathematical phrase into an expression and then simplify it.

Try It 3.51

Translate and simplify the expression:

the sum of −7−7 and 44

Try It 3.52

Translate and simplify the expression:

the sum of −8−8 and −6−6

Example 3.27

Translate and simplify: the sum of 88 and −12,−12, increased by 3.3.

Solution

The phrase increased by indicates addition.

The sum of 88 and −12−12, increased by 33
Translate. [8+(−12)]+3[8+(−12)]+3
Simplify. −4+3−4+3
Add. −1−1
Steps to translate and simplify a mathematical phrase into its numerical result.

Try It 3.53

Translate and simplify:

the sum of 99 and −16,−16, increased by 4.4.

Try It 3.54

Translate and simplify:

the sum of −8−8 and −12,−12, increased by 7.7.

Add Integers in Applications

Recall that we were introduced to some situations in everyday life that use positive and negative numbers, such as temperatures, banking, and sports. For example, a debt of $5$5 could be represented as −$5.−$5. Let’s practice translating and solving a few applications.

Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.

Example 3.28

The temperature in Buffalo, NY, one morning started at 7degrees7degrees below zero Fahrenheit. By noon, it had warmed up 12degrees.12degrees. What was the temperature at noon?

Solution

We are asked to find the temperature at noon.

Write a phrase for the temperature. The temperature warmed up 12 degrees from 7 degrees below zero.
Translate to math notation. −7 + 12
Simplify. 5
Write a sentence to answer the question. The temperature at noon was 5 degrees Fahrenheit.
Table 3.2 This table illustrates the step-by-step process of solving a temperature word problem, including phrasing, translation to math notation, simplification, and final answer sentence.

Try It 3.55

The temperature in Chicago at 5 A.M. was 10degrees10degrees below zero Celsius. Six hours later, it had warmed up 14 degrees Celsius.14 degrees Celsius. What is the temperature at 11 A.M.?

Try It 3.56

A scuba diver was swimming 16 feet16 feet below the surface and then dove down another 17 feet.17 feet. What is her new depth?

Example 3.29

A football team took possession of the football on their 42-yard line.42-yard line. In the next three plays, they lost 6 yards,6 yards, gained 4 yards,4 yards, and then lost 8 yards.8 yards. On what yard line was the ball at the end of those three plays?

Solution

We are asked to find the yard line the ball was on at the end of three plays.

Write a word phrase for the position of the ball. Start at 42, then lose 6, gain 4, lose 8.
Translate to math notation. 42 − 6 + 4 − 8
Simplify. 32
Write a sentence to answer the question. At the end of the three plays, the ball is on the 32-yard line.
Table 3.3 Illustrates problem-solving steps: converting a word phrase to math notation, simplifying, and stating the final answer for a ball's position.

Try It 3.57

The Bears took possession of the football on their 20-yard line.20-yard line. In the next three plays, they lost 9 yards,9 yards, gained 7 yards,7 yards, then lost 4 yards.4 yards. On what yard line was the ball at the end of those three plays?

Try It 3.58

The Chargers began with the football on their 25-yard line.25-yard line. They gained 5 yards,5 yards, lost 8 yards8 yards and then gained 15 yards15 yards on the next three plays. Where was the ball at the end of these plays?

Section 3.2 Exercises

Practice Makes Perfect

Model Addition of Integers

In the following exercises, model the expression to simplify.

63.

7 + 4 7 + 4

64.

8 + 5 8 + 5

65.

−6 + ( −3 ) −6 + ( −3 )

66.

−5 + ( −5 ) −5 + ( −5 )

67.

−7 + 5 −7 + 5

68.

−9 + 6 −9 + 6

69.

8 + ( −7 ) 8 + ( −7 )

70.

9 + ( −4 ) 9 + ( −4 )

Simplify Expressions with Integers

In the following exercises, simplify each expression.

71.

−21 + ( −59 ) −21 + ( −59 )

72.

−35 + ( −47 ) −35 + ( −47 )

73.

48 + ( −16 ) 48 + ( −16 )

74.

34 + ( −19 ) 34 + ( −19 )

75.

−200 + 65 −200 + 65

76.

−150 + 45 −150 + 45

77.

2 + ( −8 ) + 6 2 + ( −8 ) + 6

78.

4 + ( −9 ) + 7 4 + ( −9 ) + 7

79.

−14 + ( −12 ) + 4 −14 + ( −12 ) + 4

80.

−17 + ( −18 ) + 6 −17 + ( −18 ) + 6

81.

135 + ( −110 ) + 83 135 + ( −110 ) + 83

82.

140 + ( −75 ) + 67 140 + ( −75 ) + 67

83.

−32 + 24 + ( −6 ) + 10 −32 + 24 + ( −6 ) + 10

84.

−38 + 27 + ( −8 ) + 12 −38 + 27 + ( −8 ) + 12

85.

19 + 2 ( −3 + 8 ) 19 + 2 ( −3 + 8 )

86.

24 + 3 ( −5 + 9 ) 24 + 3 ( −5 + 9 )

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

87.

x+8x+8 when

  1. ⓐ x=−26x=−26
  2. ⓑ x=−95x=−95
88.

y+9y+9 when

  1. ⓐ y=−29y=−29
  2. ⓑ y=−84y=−84
89.

y+(−14)y+(−14) when

  1. ⓐ y=−33y=−33
  2. ⓑ y=30y=30
90.

x+(−21)x+(−21) when

  1. ⓐ x=−27x=−27
  2. ⓑ x=44x=44
91.

When a=−7,a=−7, evaluate:

  1. ⓐ a+3a+3
  2. ⓑ −a+3−a+3
92.

When b=−11,b=−11, evaluate:

  1. ⓐ b+6b+6
  2. ⓑ −b+6−b+6
93.

When c=−9,c=−9, evaluate:

  1. ⓐ c+(−4)c+(−4)
  2. ⓑ −c+(−4)−c+(−4)
94.

When d=−8,d=−8, evaluate:

  1. ⓐ d+(−9)d+(−9)
  2. ⓑ −d+(−9)−d+(−9)
95.

m+nm+n when, m=−15m=−15, n=7n=7

96.

p+qp+q when, p=−9p=−9, q=17q=17

97.

r−3sr−3s when, r=16r=16, s=2s=2

98.

2t+u2t+u when, t=−6t=−6, u=−5u=−5

99.

(a+b)2(a+b)2 when, a=−7a=−7, b=15b=15

100.

(c+d)2(c+d)2 when, c=−5c=−5, d=14d=14

101.

(x+y)2(x+y)2 when, x=−3x=−3, y=14y=14

102.

(y+z)2(y+z)2 when, y=−3y=−3, z=15z=15

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

103.

The sum of −14−14 and 55

104.

The sum of −22−22 and 99

105.

88 more than −2−2

106.

55 more than −1−1

107.

−10−10 added to −15−15

108.

−6−6 added to −20−20

109.

66 more than the sum of −1−1 and −12−12

110.

33 more than the sum of −2−2 and −8−8

111.

the sum of 1010 and −19,−19, increased by 44

112.

the sum of 1212 and −15,−15, increased by 11

Add Integers in Applications

In the following exercises, solve.

113.

Temperature The temperature in St. Paul, Minnesota was −19°F−19°F at sunrise. By noon the temperature had risen 26°F.26°F. What was the temperature at noon?

114.

Temperature The temperature in Chicago was −15°F−15°F at 6 am. By afternoon the temperature had risen 28°F.28°F. What was the afternoon temperature?

115.

Credit Cards Lupe owes $73$73 on her credit card. Then she charges $45$45 more. What is the new balance?

116.

Credit Cards Frank owes $212$212 on his credit card. Then he charges $105$105 more. What is the new balance?

117.

Football A team lost 3 yards3 yards the first play. Then they lost 2 yards,2 yards, gained 1 yard,1 yard, and then lost 4 yards.4 yards. What was the change in overall yardage over the four plays?

118.

Card Games April lost 5 cards5 cards the first turn. Over the next three turns, she lost 3 cards,3 cards, gained 2 cards,2 cards, and then lost 1 card.1 card. What was the change in cards over the four turns?

119.

Football The Rams took possession of the football on their own 35-yard line.35-yard line. In the next three plays, they lost 12 yards,12 yards, gained 8 yards,8 yards, then lost 6 yards.6 yards. On what yard line was the ball at the end of those three plays?

120.

Football The Cowboys began with the ball on their own 20-yard line.20-yard line. They gained 15 yards,15 yards, lost 3 yards3 yards and then gained 6 yards6 yards on the next three plays. Where was the ball at the end of these plays?

121.

Scuba Diving A scuba diver swimming 8 feet8 feet below the surface dove 17 feet17 feet deeper; the pressure got to them and they rose five feet. What is their new depth?

122.

Gas Consumption: Ozzie rode their motorcycle for 30 minutes,30 minutes, using 168 fluid ounces of gas.168 fluid ounces of gas. Then they stopped and got 140-fluid ounces of gas.140-fluid ounces of gas. Represent the change in gas amount as an integer.

Everyday Math

123.

Stock Market The week of September 15, 2008, was one of the most volatile weeks ever for the U.S. stock market. The change in the Dow Jones Industrial Average each day was:

Monday −504 Tuesday + 142 Wednesday −449 Thursday + 410 Friday + 369 Monday −504 Tuesday + 142 Wednesday −449 Thursday + 410 Friday + 369

What was the overall change for the week?

124.

Stock Market During the week of June 22, 2009, the change in the Dow Jones Industrial Average each day was:

Monday −201 Tuesday −16 Wednesday −23 Thursday + 172 Friday −34 Monday −201 Tuesday −16 Wednesday −23 Thursday + 172 Friday −34

What was the overall change for the week?

Writing Exercises

125.

Explain why the sum of −8−8 and 22 is negative, but the sum of 88 and −2−2 and is positive.

126.

Give an example from your life experience of adding two negative numbers.

Self Check

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

A self-assessment table for math students, allowing them to rate their confidence in skills such as modeling integer addition, simplifying expressions, evaluating variables, and translating word phrases.

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