example 2 add real numbers find the sum. rule of same signs take absolute values. = – (5.3 + 4.9)...

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EXAMPLE 2 Add real numbers Find the sum. Rule of same signs Take absolute values. = – (5.3 + 4.9) = – 10.2 Add. . – 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 )

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Page 1: 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

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 )

Page 2: 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

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

Page 3: 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

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

EXAMPLE 4Solve 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

Page 4: 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

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

Page 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

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.

ANSWERManufacturer A had the greater total profit.

Page 6: 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

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

Page 7: 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

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

Page 8: 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

GUIDED PRACTICE for Examples 2, 3 and 4

ANSWER

Manufacturer A has the greater total profit.

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