Additional Example 1A: Modeling Integer Addition Use a number line to find each 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 each 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 each sum. Check It Out: Example 1A Use a number line to find each sum. –4 + (–5) –10 –8 –6 –4 –2 0 2 –4 +(–5) –9

Use a number line to find each sum. Check It Out: Example 1B Use a number line to find each sum. 5 + (–3) 5 +(–3) 2 2 4 6 –2 0

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. 5

Additional Example 2A: Adding Integers Using Absolute Values Find each sum. –4 + (–9) The signs are the same. Find the sum of the absolute values. –4 + (–9) Think: 4 + 9. Use the sign of the two integers. –13 6

Additional Example 2B: Adding Integers Using Absolute Values Find each 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 7

Signs are the same. Find the sum of the absolute values. 13 + 24 = 37 Check It Out: Example 2A Find each sum. –13 + (–24) Signs are the same. Find the sum of the absolute values. 13 + 24 = 37 Use the sign of the integers: –37 8

Signs are different. Find the difference of the absolute values. Check It Out: Example 2B Find each sum. 11 + (–12) Signs are different. Find the difference of the absolute values. 12 – 11 = 1 Use the sign of the integer with the greater absolute value: –1 9

Additional Example 3: Evaluating Expressions with Integers Evaluate x + y for x = –42, y = 71. x + y Substitute for x and y. –42 + 71 The signs are different. Think 71 - 42 = 29 Use the sign of the integer with the greater absolute value (positive). 29 When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference. Helpful Hint

Check It Out: Example 3A Evaluate x + y for the given values. x = –24, y = 17 –24 + 17 Signs are different. Find the difference of the absolute values. 24 –17 = 7 Use the sign of the integer with the greater absolute value: –7

Check It Out: Example 3B Evaluate x + y for the given values. x = –6, y = 15 –6 + (–15) Signs are the same. Find the sum of the absolute values. 6 + 15 = 21 Use the sign of the integers: –21

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 earned $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) 730 – 52 = 678 The club’s profit was $678 14

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 15

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 16