EXAMPLE 1 Add two integers using a number line

Use a number line to find the sum.

a. – 3 + 6

ANSWER

The final position is 3. So, – 3 + 6 = 3.

EXAMPLE 1

b. – 4 + (– 5)

ANSWER

The final position is – 9. So, – 4 + (– 5) = – 9.

Add two integers using a number line

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

1. 7 +(– 2)

ANSWER

5

2. 8 +(– 11)

ANSWER

– 3

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

ANSWER

– 4

3. – 8 + 4

4. –1 + (– 4)

ANSWER

– 5

EXAMPLE 2 Add real numbers

Find the sum.

Rule of same signs

Take absolute values.= – (5.3 + 4.9)

= – 10.2 Add.

a. – 5.3 + (– 4.9)

Rule of different signs

Take absolute values. = 19.3 – 12.2

= 7.1 Subtract.

b. 19.3 + (–12.2) = 19.3 – –12.2

= – ( – 5.3 + – 4.9 )

EXAMPLE 3 Identify properties of addition

Statement Property illustrated

a. (x + 9) + 2 = x + (9 + 2) Associative property of addition

b. 8.3 + (– 8.3) = 0 Inverse property of addition

c. – y + 0.7 = 0.7 + (– y) Commutative property of addition

The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit for the three years?

EXAMPLE 4 Solve a multi-step problem

BUSINESS

Year Profit (millions) for manufacturer A

Profit (millions) for manufacturer B

1 – $5.8 – $6.5

2 $8.7 $7.9

3 $6.8 $8.2

SOLUTION

EXAMPLE 4

Solve a multi-step problem

STEP 1Calculate the total profit for each manufacturer.

Manufacturer A:

Total profit = – 5.8 + 8.7 + 6.8

= – 5.8 + (8.7 + 6.8)

= – 5.8 + 15.5

= 9.7

EXAMPLE 4

Solve a multi-step problem

Manufacturer B:

Total profit = – 6.5 + 7.9 + 8.2= – 6.5 + (7.9 + 8.2)

= – 6.5 + 16.1

= 9.6

STEP 2Compare the total profits: 9.7 > 9.6.

ANSWER

Manufacturer A had the greater total profit.

GUIDED PRACTICE for Examples 2, 3 and 4

Find the sum.

= – 7.35. – 0.6 + (– 6.7)

= – 6.16. 10.1 + (– 16.2)

7. – 13.1 + 8.7 = – 4.4

Identify the property being illustrated.

8. 7 + (– 7) = 0 Inverse property of addition

9. – 12 + 0 = – 12 Identity property of addition

10. 4 + 8 = 8 + 4 Commutative property of addition

GUIDED PRACTICE for Examples 2, 3 and 4

11.

WHAT IF? In Example 4, suppose that the profits for year 4 are – $1.7 million for manufacturer A and – $2.1 million for manufacturer B. Which manufacturer has the greater total profit for the four years?

Year Profit (millions) for manufacturer A

Profit (millions) for manufacturer B

1 – $5.8 – $6.5

2 $8.7 $7.9

3 $6.8 $8.2

4 – $1.7 – $2.1

GUIDED PRACTICE for Examples 2, 3 and 4

ANSWER

Manufacturer A has the greater total profit.