Preview Warm Up California Standards Lesson Presentation

Warm Up Find each absolute value. 1. |8| 2. |–6| 3. |–9| 8 4. |–7| 5. |–12| 6. |53| 8 6 9 7 12 53

NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Also covered: AF1.2 California Standards

Additional Example 1A: Modeling Integer Addition Use a number line to find the sum. –7 + (–4) +(–4) –7 2 –14 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 7 spaces. Then move left 4 more spaces. –7 + (–4) = –11

Additional Example 1B: Modeling Integer Addition Use a number line to find the sum. –12 + 19 19 –12 2 4 6 8 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 12 spaces. Then move right 19 spaces. –12 + 19 = 7

Use a number line to find the sum. Check It Out! Example 1A Use a number line to find the sum. –4 + (–5) +(–5) –4 2 –14 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 4 spaces. Then move left 5 more spaces. –4 + (–5) = –9

Use a number line to find the sum. Check It Out! Example 1B Use a number line to find the sum. –7 + 12 12 –7 2 4 6 8 –12 –10 –8 –6 –4 –2 0 Start at 0. Move left 7 spaces. Then move right 12 spaces. –7 + 12 = 5

Adding Integers To add two integers with the same sign, find the sum of their absolute values. Use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values. Use the sign of the integer with the greater absolute value.

Additional Example 2A: Adding Integers Using Absolute Values Find the sum. –4 + 8 The signs are different. Find the difference of the absolute values. –4 + 8 Think: 8 – 4 = 4. Use the sign of the integer with the greater absolute value. 4 When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference. Helpful Hint

Additional Example 2B: Adding Integers Using Absolute Values Find the sum. 23 + (–35) The signs are different. Find the difference of the absolute values. 23 + (–35) Think: 35 – 23 = 12. Use the sign of the integer with the greater absolute value. –12

Check It Out! Example 2A Find the sum. –5 + 3 The signs are different. Find the difference of the absolute values. –5 + 3 Think: 5 – 3 = 2. Use the sign of the integer with the greater absolute value. –2

Check It Out! Example 2B Find the sum. –13 + (–24) The signs are the same. Find the sum of the absolute values. –13 + (–24) Think: 13 + 24 = 37. –37 Use the sign of the two integers.

Additional Example 3: Evaluating Expressions with Integers Evaluate x + y for x = –42 and y = 71. x + y Substitute for –42 for x and 71 for y. –42 + 71 The signs are different. Think: 71 – 42 = 29 Use the sign of the integer with the greater absolute value (positive). 29

Check It Out! Example 3 Evaluate x + y for x = –24 and y = 17. x + y Substitute for –24 for x and 17 for y. –24 + 17 The signs are different. Think: 24 – 17 = 7. Use the sign of the integer with the greater absolute value (negative). –7

Additional Example 4: Application The jazz band’s income from a bake sale was $286. Expenses were $21. Use integer addition to find the band’s total profit or loss. 286 + (–21) Use negative for the expenses. Find the difference of the absolute values. 286 – 21 265 The answer is positive. The band's profit was $265.

Check It Out! Example 4 The French Club was raising money for a trip to Washington, D.C. Their car wash raised $730. They had expenses of $52. Use integer addition to find the club’s total profit or loss. 730 + (–52) Use negative for the expenses. Find the difference of the absolute values. 730 – 52 678 The answer is positive. The club's profit was $678.

Use a number line to find the sum. 1. –7 + (–6) Lesson Quiz: Part I Use a number line to find the sum. 1. –7 + (–6) Find each sum. 2. –15 + 24 + (–9) 3. –24 + 7 + (–3) 4. Evaluate x + y for x = –2 and y = –15. –13 2 –14 –12 –10 –8 –6 –4 –2 0 –20 –17

Lesson Quiz: Part II 5. The math club’s income from a bake sale was $217. Advertising expenses were $32. Use integer addition to find the club’s total profit or loss? $185 profit