Chapter1.4
- 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
- 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