1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Graph each number on a number line. 1. –5 2. 7 3. –4 4. 0 – 5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

3. NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used. California Standards

4. Vocabulary additive inverse

5. Additional Example 1A: Using a Number Line to Add Integers Use a number line to find the sum. (–6) + 2 – 6 You finish at –4, so (–6) + 2 = –4. Start at 0. Move left 6 units. From –6, move right 2 units. To add a positive number move to the right . To add a negative number move to the left . Helpful Hint 2 – 6 –5 –4 –3 –2 –1 0 1 2 3 4 5

6. Additional Example 1B: Using a Number Line to Add Integers Use a number line to find the sum. – 3 + (–6) – 6 You finish at –9, so –3 + (–6) = –9. Start at 0. Move left 3 units. From –3, move left 6 units. – 3 – 9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

7. Check It Out! Example 1A Use a number line to find the sum. (–3) + 7 – 3 You finish at 4, so (–3) + 7 = 4. Start at 0. Move left 3 units. From –3, move right 7 units. 7 – 6 –5 –4 –3 –2 –1 0 1 2 3 4 5

8. Check It Out! Example 1B Use a number line to find the sum. (–2) + 4 – 2 You finish at 2, so (–2) + 4 = 2. Start at 0. Move left 2 units. From –2, move right 4 units. 4 – 6 –5 –4 –3 –2 –1 0 1 2 3 4 5

9. Another way to add integers is to use absolute value.

10. Additional Example 2: Using Absolute Value to Add Integers A. 1 + (–2) Add. 1 + (–2) 2 > 1; use the sign of 2. – 1 B. (–8) + 5 (–8) + 5 8 > 5; use the sign of 8. – 3 Think: Find the difference of 1 and –2 . Think: Find the difference of –8 and 5 .

11. Additional Example 2: Using Absolute Value to Add Integers C. (–2) + (–4) Add. (–2) + (–4) Same sign; use the sign of the integers. – 6 Think: Find the sum of –2 and –4 .

12. Check It Out! Example 2 A. 3 + (–6) Add. 3 + (–6) 6 > 3; use the sign of 6. – 3 B. (–4) + 1 (–4) + 1 4 > 1; use the sign of 4. – 3 Think: Find the difference of 3 and –6 . Think: Find the difference of –4 and 1 .

13. Check It Out! Example 2 C. (–6) + (–7) Add. (–6) + (–7) Same sign; use the sign of the integers. – 13 Think: Find the sum of –6 and –7 .

14. Additional Example 3: Evaluating Expressions with Integers Evaluate c + 4 for c = –8. c + 4 Replace c with –8. 8 > 4; use the sign of 8. (–8) + 4 – 8 + 4 = –4 Think: Find the difference of –8 and 4 .

15. Check It Out! Example 3 Evaluate d + 7 for d = –3. d + 7 Replace d with –3. 7 > 3; use the sign of 7. (–3) + 7 – 3 + 7 = 4 Think: Find the difference of –3 and 7 .

16. Additional Example 4: Application Meka opened a new bank account. Find her account balance after the first four transactions listed below. Deposits: $200, $20 Withdrawals: $166, $38 Use a positive sign for deposits and a negative sign for withdrawals. 200 + 20 + ( –166 ) + ( –38 ) Group integers with the same signs. (200 + 20) + ( –166 + –38 ) Add integers within each group. 220 + ( –204 ) 220 > 204; use the sign of 220. 16 Meka’s account balance after the first four transactions is $16.

17. Check It Out! Example 4 Michael opened a new bank account. Find his account balance after the first four transactions listed below. Deposits: $175, $95 Withdrawals: $133, $65 Use a positive sign for deposits and a negative sign for withdrawals. 175 + 95 + ( –133 ) + ( –65 ) Group integers with the same signs. (175 + 95) + ( –133 + –65 ) Add integers within each group. 270 + ( –198 ) 270 > 198; use the sign of 270. 72 Michael’s account balance after the first four transactions is $72.

18. Lesson Quiz Add. 1. –7 + (–7) 2. 15 + (–9) + (–2) 4 – 14 Evaluate each expression for the given value of the variable. 3. 13 + r for r = –15 4. 2 + b + (–9) for b = –6 – 2 – 13 5. On Monday, a local dog shelter had six dogs. By Friday, they had found homes for three, but took in two more. Then how many dogs were in the shelter? 5 dogs