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Use a number line to find the sum.

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

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Use a number line to find the sum.

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

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

  3. 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.

  4. Helpful Hint When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference. 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

  5. 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. (negative) –12

  6. 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. The signs are different. Think: 71 – 42 = 29 –42 + 71 Use the sign of the integer with the greater absolute value (positive). 29

  7. 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.

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

  9. Check It Out! Example 2 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.

  10. 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. The signs are different. Think: 24 – 17 = 7. –24 + 17 Use the sign of the integer with the greater absolute value (negative). –7

  11. 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.

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