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2-1 Adding Integers Warm Up Problem of the Day Lesson Presentation Pre-Algebra 2-1 Adding Integers Warm Up Graph each number on a number line. 1. 5 2. 7 3. 4 4. 0 0 1 2 3 Add. 5. 22 + 19 41 Pre-Algebra 4 5 6 7 8 9 10 6. 17 + 18 35 2-1 Adding Integers Problem of the Day Start at (0, 0). Walk 3 blocks west and 2 blocks north. Then walk 4 blocks south and 1 block east. What are your coordinates? (–2, –2) Pre-Algebra 2-1 Adding Integers Learn to add integers. Pre-Algebra 2-1 Adding Insert Lesson Title Here Integers Vocabulary integer opposite absolute value Pre-Algebra 2-1 Adding Integers Integers are sets of whole numbers, including 0, and their opposites. The sum of two opposite integers is zero. –3 and 3 are opposites -5 -4 -3 -2 -1 Negative integers 0 1 2 3 5 Positive integers 0 is its own opposite Pre-Algebra 4 2-1 Adding Integers Additional Example 1: Using a Number Line to Add Integers Use a number line to find the sum. (–6) + 2 –6 2 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 You finish at –4, so (–6) + 2 = –4. Helpful Hint To add a positive number move to the right. To add a negative number move to the left. Pre-Algebra 2-1 Adding Integers Try This: Example 1 Use a number line to find the sum. (–3) + 7 –3 7 –6 –5 –4 –3 –2 –1 0 1 2 You finish at 4, so (–3) + 7 = 4. Pre-Algebra 3 4 5 2-1 Adding Integers Another way to add integers is to use absolute value. The absolute value of a number is its distance from 0. The absolute value of –4, written as |–4|, is 4; and the absolute value of 5 is 5. Adding integers If the signs are the same. . . If the signs are different. . . find the sum of the absolute values. Use the same sign as the integers. find the difference of the absolute values. Use the sign of the integer with the larger absolute value. Pre-Algebra 2-1 Adding Integers Additional Example 2A & 2B: Using Absolute Value to Add Integers Add. A. 1 + (–2) 1 + (–2) –1 Think: Find the difference of 2 and 1. 2 > 1; use the sign of 2. B. (–8) + 5 (–8) + 5 –3 Pre-Algebra Think: Find the difference of 8 and 5. 8 > 5; use the sign of 8. 2-1 Adding Integers Additional Example 2C: Using Absolute Value to Add Integers Add. C. (–2) + (–4) (–2) + (–4) Think: Find the sum of 2 and 4. –6 Same sign; use the sign of the integers. Pre-Algebra 2-1 Adding Integers Try This: Example 2A & 2B Add. A. 3 + (–6) 3 + (–6) –3 Think: Find the difference of 6 and 3. 6 > 3; use the sign of 6. B. (–4) + 1 (–4) + 1 –3 Pre-Algebra Think: Find the difference of 4 and 1. 4 > 1; use the sign of 4. 2-1 Adding Integers Try This: Example 2C Add. C. (–6) + (–7) (–6) + (–7) Think: Find the sum of 6 and 7. –13 Same sign; use the sign of the integers. Pre-Algebra 2-1 Adding Integers Additional Example 3: Evaluating Expressions with Integers Evaluate c + 4 for c = –8. c+4 (–8) + 4 Replace c with –8. Think: Find the difference of 8 and 4. –8 + 4 = –4 8 > 4; use the sign of 8. Pre-Algebra 2-1 Adding Integers Try This: Example 3 Evaluate d + 7 for d = –3. d+7 (–3) + 7 Replace d with –3. Think: Find the difference of 7 and 3. –3 + 7 = 4 7 > 3; use the sign of 7. Pre-Algebra 2-1 Adding Integers Additional Example 4: Application Katrina opened a new bank account. Find her account balance after the first four transactions listed below. Deposits: $200, $20 Withdrawals: $166, $38 200 + 20 + (–166) + (–38) (200 + 20) + (–166 + –38) 220 + (–204) Use a positive sign for deposits and a negative sign for withdrawals. Group integers with same signs. Add integers within each group. 220 > 204; use the sign of 220. Katrina’s account balance after the first four transactions is $16. 16 Pre-Algebra 2-1 Adding Integers Try This: Example 4 Michael opened a new bank account. Find his account balance after the first four transactions listed below. Deposits: $175, $95 Withdrawals: $133, $65 175 + 95 + (–133) + (–65) (175 + 95) + (–133 + –65) 270 + (–198) 72 Use a positive sign for deposits and a negative sign for withdrawals. Group integers with same signs. Add integers within each group. 270 > 198; use the sign of 270. Michael’s account balance after the first four transactions is $72. Pre-Algebra 2-1 Adding Integers Insert Lesson Title Here Lesson Quiz: Part 1 Add. 1. –7 + (– 7) –14 2. 15 + (–9) + (–2) 4 Evaluate each expression for the given value of the variable. 3. 13 + r for r = –15 –2 4. 2 + b + (–9) for b = –6 –13 Pre-Algebra 2-1 Adding Integers Insert Lesson Title Here Lesson Quiz: Part 2 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 Pre-Algebra