2.2 add real numbers 1

1. Add Real Numbers Section 2.2 P. 74 -79

2. Properties of Addition Commutative Property : - the order in which two numbers are added does NOT change the sum. 4 + -8 = -8 + 4 Associative Property : The way you group three numbers when adding does NOT change the sum. (-5 + 8) + 9 = -5 + ( 8 + 9 )

3. Properties of Addition Identity Property : The sum of a number and zero is always the number. -9 + 0 = -9 x + 0 = x Inverse Property: The sum of a number and its opposite is 0. a + (- a ) = 0 -4 + 4 = 0

4. 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.

5. EXAMPLE 1 b . – 4 + (– 5) ANSWER The final position is – 9 . So , – 4 + ( – 5 ) = – 9. Add two integers using a number line

6. GUIDED PRACTICE for Example 1 Use a number line to find the sum . 1. 7 +(– 2) ANSWER The final position is 3 . So , 7 +(– 2) = 5. Move Units to the left . – 2 End at 5 Start at 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

7. GUIDED PRACTICE for Example 1 Use a number line to find the sum . 2. 8 +(– 11) ANSWER The final position is – 3 . So , 8 +(– 11) = – 3. -11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 End at - 3 Start at 8 Move Units to the left . – 11

8. GUIDED PRACTICE for Example 1 Use a number line to find the sum . 3. – 8 + (4) ANSWER The final position is – 4 . So , – 8 +4 = – 4. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Start at - 8 End at - 4 Move Units to the right . – 2 Move Units to the right . 4

9. GUIDED PRACTICE for Example 1 Use a number line to find the sum . 3. –1 + (– 4) ANSWER The final position is – 5 . So , – 1 + (– 4) = – 5. Move Units to the right . – 2 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 Start at – 1 End at – 5 Move Units to the left . – 4

10. EXAMPLE 2 Add real numbers Find the sum. Rule of same signs Take absolute values. = – (5.3 + 4.9) = – 1 0.2 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)

11. 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

12. 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

13. SOLUTION EXAMPLE 4 Solve a multi-step problem 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