Preview Warm Up California Standards Lesson Presentation

Warm Up Multiply or divide. 1. 5(8) 40 2. 6(12) 72 36 9 49 7 3. 4 4. 7 192 16 12 5. 18(7) 126 6.

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

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.

3(–10) = 2(–10) = 1(–10) = 0(–10) = –1(–10) = –2(–10) = –3(–10) = 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 + 10 –20 + 10 –10 + 10 + 10 10 + 10 20 + 10 30

Additional Example 1: Multiplying and Dividing Integers Multiply or divide. A. –6(4) Signs are different. –24 Answer is negative. B. –8(–5)(2) Multiply two integers. –8(–5)(2) Signs are the same. 40(2) Answer is positive. 40(2) Signs are the same. 80 Answer is positive.

Additional Example 1: Multiplying and Dividing Integers Multiply or divide. –18 2 C. Signs are different. –9 Answer is negative. –25 –5 D. Signs are the same. 5 Answer is positive.

Check It Out! Example 1 Multiply or divide. A. 5(–2) Signs are different. –10 Answer is negative. B. –3(–2)(4) –3(–2)(4) Signs are the same. 6(4) Answer is positive. 6(4) Signs are the same. 24 Answer is positive.

Check It Out! Example 1 Multiply or divide. –24 3 C. Signs are different. –8 Answer is negative. –12 –2 D. Signs are the same. 6 Answer is positive.

Additional Example 2: Using the Order of Operations with Integers Simplify. A. 3(–6 – 12) Subtract inside the parentheses. Add the opposite of 12 inside the parentheses. 3(–6 + –12) 3(–18) Think: The signs are different. –54 The answer is negative. B. –5(–5 + 2) Add inside the parentheses. –5(–3) Think: The signs are the same. 15 The answer is positive.

Additional Example 2: Using the Order of Operations with Integers Simplify. C. –2(14) – 5 Multiply. Same sign; use the sign of the integers. –28 – 5 –33 The answer is negative.

Check It Out! Example 2 Simplify. A. 2(1 – 8) Subtract inside the parentheses. Add the opposite of 8 inside the parentheses. 2(1 + –8) 2(–7) Think: The signs are different. –14 The answer is negative. B. 4(–3 – 8) Subtract inside the parentheses. 4(–11) Think: The signs are different. –44 The answer is negative.

Check It Out! Example 2 Simplify. C. –3(6) – 9 Multiply. Same sign; use the sign of the integers. –18 – 9 –27 The answer is negative.

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) Add the strokes over par to under par. 12 + (–8) Multiply. 4 Add. The golfer's score was 4 over par.

Check It Out! Example 3 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. 3(3) + 4(–3) Add the strokes over par to under par. 9 + (–12) Multiply. –3 Add. The golfer's score was 3 under par.

Lesson Quiz Multiply or divide. 1. –8(4) –32 2. –12(5) –10 6 Simplify. 3. –2(13 – 4) –18 4. 6(–5 – 3) –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