2-2 Adding Integers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-2 Adding Integers

Warm UpFind each absolute value.

1. |8|

2. |–6|

3. |–9|

4. |–7|

5. |–12|

6. |53|

8

69

7

12

53

2-2 Adding Integers

Problem of the Day

Jan’s yearly salary is $30,000, and it will be increased by $3,000 each year. Phil’s salary is $20,000, and it will be increased by $5,000 each year. In how many years will Jan and Phil both have the same yearly salary?5 years

2-2 Adding Integers

I can add integers.

2-2 Adding Integers

Use a number line to find each sum.

Additional Example 1A: Modeling Integer Addition

2 –14 –12 –10 –8 –6 –4 –2 0

–7 + (–4)–7+(–4)

–7 + (–4) = –11

Start at 0. Move left 7 spaces. Then move left4 more spaces.

2-2 Adding Integers

Use a number line to find each sum.

Additional Example 1B: Modeling Integer Addition

–12 + 19

–12

19

–12 + 19 = 7

Start at 0. Move left 12 spaces. Then move right 19 spaces.

2 4 6 8

–12 –10 –8 –6 –4 –2 0

2-2 Adding Integers

Check It Out: Example 1A

Use a number line to find each sum.

2 –14 –12 –10 –8 –6 –4 –2 0

–4 + (–5)–4+(–5)

–4 + (–5) = –9

Start at 0. Move left 4 spaces. Then move left5 more spaces.

2-2 Adding Integers

Check It Out: Example 1B

Use a number line to find each sum.

–7 + 12

–7

12

–7 + 12 = 5

Start at 0. Move left 7 spaces. Then move right 12 spaces.

2 4 6 8

–12 –10 –8 –6 –4 –2 0

2-2 Adding Integers

Adding IntegersAdding Integers

To add two integers with the same sign, find the sum of their absolute values. Use the sign of the two integers.

To add two integers with different signs, find the difference of their absolute values. Use the sign of the integer with the greater absolute value.

2-2 Adding Integers

Find each sum.

Additional Example 2A: Adding Integers Using Absolute Values

–4 + 8

–4 + 8

The signs are different. Find the difference of the absolute values.

Think: 8 – 4 = 4.

Use the sign of the integer with the greater absolute value.

4

2-2 Adding Integers

Additional Example 2B: Adding Integers Using Absolute Values

Find each sum.

23 + (–35)

23 + (–35)

The signs are different. Find the difference of the absolute values.

Think: 35 – 23 = 12.

Use the sign of the integer with the greater absolute value.

–12

2-2 Adding Integers

Check It Out: Example 2A

Find each sum.

–5 + 3

–5 + 3 Think: 5 – 3 = 2.

Use the sign of the integer with the greater absolute value.

–2

The signs are different. Find the difference of the absolute values.

2-2 Adding Integers

Check It Out: Example 2B

Find each sum.

–13 + (–24)

–13 + (–24)

The signs are the same. Find the sum of the absolute values.

Think: 13 + 24 = 37.

Use the sign of the two integers.–37

2-2 Adding Integers

Evaluate x + y for x = –42, y = 71.

Additional Example 3: Evaluating Expressions with Integers

x + y

–42 + 71

Substitute for x and y.

The signs are different. Think 71- 42 = 29

Use the sign of the integer with the greater absolute value (positive).29

When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference.

Helpful Hint

2-2 Adding Integers

Check It Out: Example 3

Evaluate x + y for x = –24, y = 17.

x + y

–24 + 17

Substitute for x and y.

The signs are different. Think: 24 – 17 = 7.

Use the sign of the integer with the greater absolute value (negative).

–7

2-2 Adding Integers

The jazz band’s income from a bake sale was $286. Expenses were $21. Use integer addition to find the band’s total profit or loss.

Additional Example 4: Application

286 + (–21)

286 – 21

265

The band earned $265.

Use negative for the expenses.

Find the difference of the absolute values.

The answer is positive.

2-2 Adding Integers

Check It Out: Example 4

The French Club was raising money for a trip to Washington D.C. Their car wash raised $730. They had expenses of $52. Use integer addition to find the club’s total profit or loss.

730 + (–52)

730 – 52

678

The club earned $678.

Use negative for the expenses.

Find the difference of the absolute values.

The answer is positive.

2-2 Adding Integers

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-2 Adding Integers

Lesson Quiz: Part I

Use a number line to find the sum.

1. –7 + (–6)

Find each sum.

2. –15 + 24 + (–9)

3. –24 + 7 + (–3)

4. Evaluate x + y for x = –2 and y = –15.

0

–13

–20

–17

2 –14 –12 –10 –8 –6 –4 –2 0

2-2 Adding Integers

Lesson Quiz: Part II

5. The math club’s income from a bake sale was $217. Advertising expenses were $32. Use integer addition to find the club’s total profit or loss?

$185 profit

2-2 Adding Integers

1. Identify the number line that helps to find the sum.

–5 + (–4)

A. –1

B. –9

Lesson Quiz for Student Response Systems

2-2 Adding Integers

2. Identify the sum.

–18 + 26 + (–8)

A. –36

B. 0

C. 36

D. 52

Lesson Quiz for Student Response Systems

2-2 Adding Integers

3. Identify the sum.

–26 + 8 + (–5)

A. –23

B. –13

C. 0

D. 23

Lesson Quiz for Student Response Systems

2-2 Adding Integers

4. Evaluate x + y for x = –5 and y = –17.

A. 22

B. 12

C. –12

D. –22

Lesson Quiz for Student Response Systems

2-2 Adding Integers

5. The cost of a guitar is $456. Helen has $178 with her. Use integer addition to identify how much more money she needs to buy the guitar.

A. $296

B. $278

C. $196

D. $116

Lesson Quiz for Student Response Systems