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2-2 Adding Integers California Standards 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 Holt CA Course 1 2-2 Adding Integers Additional Example 1A: Modeling Integer Addition Use a number line to find the sum. –7 + (–4) –14 –12 –7 +(–4) –10 –8 –6 –4 –2 0 2 Start at 0. Move left 7 units. Then move left 4 more units. –7 + (–4) = –11 Holt CA Course 1 2-2 Adding Integers Additional Example 1B: Modeling Integer Addition Use a number line to find the sum. –12 + 19 19 –12 –12 –10 –8 –6 –4 –2 0 2 4 6 Start at 0. Move left 12 units. Then move right 19 units. –12 + 19 = 7 Holt CA Course 1 8 2-2 Adding Integers 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. Holt CA Course 1 2-2 Adding Integers 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 Helpful Hint When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference. Holt CA Course 1 2-2 Adding Integers 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) –12 Holt CA Course 1 Think: 35 – 23 = 12. Use the sign of the integer with the greater absolute value (negative). 2-2 Adding Integers Additional Example 3: Evaluating Expressions with Integers Evaluate x + y for x = –42 and y = 71. x+y –42 + 71 29 Holt CA Course 1 Substitute for –42 for x and 71 for y. The signs are different. Think: 71 – 42 = 29 Use the sign of the integer with the greater absolute value (positive). 2-2 Adding Integers 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) 286 – 21 265 Use negative for the expenses. Find the difference of the absolute values. The answer is positive. The band's profit was $265. Holt CA Course 1 2-2 Adding Integers Check It Out! Example 1 Use a number line to find the sum. –4 + (–5) –14 –12 –10 –4 +(–5) –8 –6 –4 –2 0 2 Start at 0. Move left 4 spaces. Then move left 5 more spaces. –4 + (–5) = –9 Holt CA Course 1 2-2 Adding Integers 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 Holt CA Course 1 Use the sign of the two integers. 2-2 Adding Integers Check It Out! Example 3 Evaluate x + y for x = –24 and y = 17. x+y –24 + 17 –7 Holt CA Course 1 Substitute for –24 for x and 17 for y. The signs are different. Think: 24 – 17 = 7. Use the sign of the integer with the greater absolute value (negative). 2-2 Adding Integers 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 Use negative for the expenses. Find the difference of the absolute values. The answer is positive. The club's profit was $678. Holt CA Course 1