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NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. California Standards
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If a football team loses 10 yards in each of 3 plays, the total change in yards can be represented by 3(–10). You can write this product as repeated addition. 3(–10) = –10 + (–10) + (–10) = –30 Notice that a positive integer multiplied by a negative integer gives a negative product .
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You already know that the product of two positive integers is a positive integer. The pattern shown at right can help you understand that the product of two negative integers is also a positive integer. – 30 – 20 + 10 – 10 0 10 20 30 + 10 + 10 + 10 + 10 + 10 3(–10) = 2(–10) = 1(–10) = 0(–10) = – 1(–10) = – 2(–10) = – 3(–10) =
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Additional Example 1: Multiplying and Dividing Integers A. –6(4) B. –8(–5)(2) 40(2) – 24 Signs are different. Multiply two integers. Answer is negative . Answer is positive . Multiply or divide. – 8(–5)(2) Signs are the same. 40(2) Signs are the same. Answer is positive . 80
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Additional Example 1: Multiplying and Dividing Integers C. – 9 Signs are different. Answer is negative . Multiply or divide. D. 5 Signs are the same. Answer is positive . – 18 2 – 25 – 5
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Check It Out! Example 1 A. 5(–2) B. –3(–2)(4) 6(4) – 10 Signs are different. Signs are the same. Answer is negative . Answer is positive . Multiply or divide. – 3(–2)(4) Signs are the same. 6(4) 24 Answer is positive .
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Check It Out! Example 1 C. – 8 Signs are different. Answer is negative . Multiply or divide. D. 6 Signs are the same. Answer is positive . – 24 3 – 12 – 2
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Additional Example 2: Using the Order of Operations with Integers A. 3(–6 – 12) – 54 3(–18) Add the opposite of 12 inside the parentheses. Think: The signs are different. The answer is negative. Simplify. B. –5(–5 + 2) 15 – 5(–3) Add inside the parentheses. Think: The signs are the same. The answer is positive. 3(–6 + –12) Subtract inside the parentheses.
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Additional Example 2: Using the Order of Operations with Integers C. –2(14) – 5 – 33 – 28 – 5 Multiply. Same sign; use the sign of the integers. The answer is negative. Simplify.
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Check It Out! Example 2 A. 2(1 – 8) – 14 2(–7) Subtract inside the parentheses. Think: The signs are different. The answer is negative. Simplify. B. 4(–3 – 8) – 44 4(–11) Subtract inside the parentheses. Think: The signs are different. The answer is negative. 2(1 + –8) Add the opposite of 8 inside the parentheses.
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Check It Out! Example 2 C. –3(6) – 9 – 27 – 18 – 9 Multiply. Same sign; use the sign of the integers. The answer is negative. Simplify.
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Additional Example 3: Sports Application A golfer plays 5 holes . On 3 holes, he is 4 strokes over par. On 2 holes, he is 4 strokes under par. Each score over par can be represented by a positive integer, and each score under par can be represented by a negative integer. Find the total score relative to par. 3(4) + 2(–4) 4 12 + (–8) Add the strokes over par to under par. Multiply. Add. The golfer's score was 4 over par.
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Check It Out! Example 3 3(3) + 4(–3) – 3 9 + (–12) Add the strokes over par to under par. Multiply. Add. The golfer's score was 3 under par. A golfer plays 7 holes . On 3 holes, he has a gain of 3 strokes. On 4 holes, he is 3 strokes under par. Each score over par can be represented by a positive integer, and each score under par can be represented by a negative integer. Find the total score relative to par.
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Lesson Quiz Multiply or divide. 1. –8(4) 2. – 32 6 Simplify. 3. –2(13 – 4) 4. 6(–5 – 3) – 18 – 48 5. Evin completes 11 transactions in his bank account. In 6 transactions, he withdraws $10. In 5 transactions, he deposits $20. Find the total net change in dollars. $40 – 12(5) – 10
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