EXAMPLE 1 Add two integers using a number line

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Presentation transcript:

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 Add two integers using a number line b. – 4 + (– 5) ANSWER The final position is – 9. So, – 4 + (– 5) = – 9.

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. 3. – 8 + 4 ANSWER – 4 4. –1 + (– 4) ANSWER – 5

EXAMPLE 2 Add real numbers Find the sum. a. – 5.3 + (– 4.9) = – ( – 5.3 + – 4.9 ) Rule of same signs = – (5.3 + 4.9) Take absolute values. = – 10.2 Add. b. 19.3 + (–12.2) = 19.3 – –12.2 Rule of different signs = 19.3 – 12.2 Take absolute values. = 7.1 Subtract.

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

Profit (millions) for manufacturer A EXAMPLE 4 Solve a multi-step problem BUSINESS The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit for the three 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

EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Calculate 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 2 Compare 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. 5. – 0.6 + (– 6.7) = – 7.3 6. 10.1 + (– 16.2) = – 6.1 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

Profit (millions) for manufacturer A 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.