1. 3-5 Multiplying and Dividing Integers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Evaluate each expression. 1. 17 · 5 2. 8 · 34 3. 4 · 86 4. 20 · 850 5. 275 ÷ 5 6. 112 ÷ 4 85 272 344 Course 2 3-5 Multiplying and Dividing Integers 17,000 55 28

3. Problem of the Day To discourage guessing on a multiple choice test, a teacher assigns 5 points for a correct answer, and –2 points for an incorrect answer, and 0 points for leaving the questioned unanswered. What is the score for a student who had 22 correct answers, 15 incorrect answers, and 7 unanswered questions? 80 Course 2 3-5 Multiplying and Dividing Integers

4. Learn to multiply and divide integers. Course 2 3-5 Multiplying and Dividing Integers

5. Course 2 3-5 Multiplying and Dividing Integers You can think of multiplication as repeated addition. 3 · 2 = 2 + 2 + 2 = 6 and 3 · (–2) = (–2) + (–2) + (–2) = –6

6. Find each product. Additional Example 1: Multiplying Integers Using Repeated Addition Course 2 3-5 Multiplying and Dividing Integers A. –7 · 2 –7 · 2 = (–7) + (–7) = –14 B. –8 · 3 –8 · 3 = (–8) + (–8) + (–8) = –24 Think: –7 · 2 = 2 · –7, or 2 groups of –7. Think: –8 · 3 = 3 · –8, or 3 groups of –8.

7. Try This: Example 1 Insert Lesson Title Here Course 2 3-5 Multiplying and Dividing Integers Find each product. A. –3 · 2 –3 · 2 = (–3) + (–3) = –6 B. –5 · 3 –5 · 3 = (–5) + (–5) + (–5) = –15 Think: –3 · 2 = 2 · –3, or 2 groups of –3. Think: –5 · 3 = 3 · –5, or 3 groups of –5.

8. Course 2 3-5 Multiplying and Dividing Integers The Commutative Property of Multiplication states that order does not matter when you multiply. Remember!

9. Course 2 3-5 Multiplying and Dividing Integers Example 1 suggests that when the signs of two numbers are different, the product is negative. To decide what happens when both numbers are negative, look at the pattern at right. Notice that each product is 3 more than the preceding one. This pattern suggests that the product of two negative integers is positive. –3 · (2) = –6 –3 · (1) = –3 –3 · (0) = 0 –3 · (–1) = 3 –3 · (–2) = 6

10. Multiply. Additional Example 2: Multiplying Integers Course 2 3-5 Multiplying and Dividing Integers –6 · (–5) –6 · (–5) = 30 Both signs are negative, so the product is positive.

11. Try This: Example 2 Insert Lesson Title Here Course 2 3-5 Multiplying and Dividing Integers Multiply. –2 · (–8) –2 · (–8) = 16 Both signs are negative, so the product is positive.

12. Course 2 3-5 Multiplying and Dividing Integers Multiplication and division are inverse operations. They “undo” each other. You can use this fact to discover the rules for division of integers.

13. Course 2 3-5 Multiplying and Dividing Integers Same signsPositive Different signsNegative The rule for division is like the rule for multiplication. 4 (–2) = –8 –4 (–2) = 8 –8 ÷ (–2) = 4 8 ÷ (–2) = –4

14. Course 2 3-5 Multiplying and Dividing Integers MULTIPLYING AND DIVIDING INTEGERS If the signs are:Your answer will be: the same different positive negative

15. Find each quotient. Additional Example 3A & 3B: Dividing Integers Course 2 3-5 Multiplying and Dividing Integers A. –27 ÷ 9 –27 ÷ 9 –3 B. 35 ÷ (–5) 35 ÷ (–5) –7 Think: 27 ÷ 9 = 3. The signs are different, so the quotient is negative. Think: 35 ÷ 5 = 7. The signs are different, so the quotient is negative.

16. Additional Example 3C: Dividing Integers Course 2 3-5 Multiplying and Dividing Integers Find the quotient. C. –32 ÷ (–8) –32 ÷ –8 4 Think: 32 ÷ 8 = 4. The signs are the same, so the quotient is positive.

17. Try This: Example 1A & 1B Insert Lesson Title Here Course 2 3-5 Multiplying and Dividing Integers Find each quotient. A. –12 ÷ 3 –12 ÷ 3 –4 B. 45 ÷ (–9) 45 ÷ (–9) –5 Think: 12 ÷ 3 = 4. The signs are different, so the quotient is negative. Think: 45 ÷ 9 = 5. The signs are different, so the quotient is negative.

18. Try This: Example 3C Insert Lesson Title Here Course 2 3-5 Multiplying and Dividing Integers Find the quotient. C. –25 ÷ (–5) –25 ÷ –5 5 Think: 25 ÷ 5 = 5. The signs are the same, so the quotient is positive.

19. Mrs. Johnson kept track of a stock she was considering buying. She recorded the price change each day. What was the average change per day? Additional Example 4: Averaging Integers Course 2 3-5 Multiplying and Dividing Integers Day MonTueWedThuFri Price Change ($) –$1$3$2–$5$6 (–1) + 3 + 2 + (–5) + 6 = 5 Find the sum of the changes in price. 5555 = 1 The average change per day was $1. Divide to find the average.

20. Try This: Example 4 Insert Lesson Title Here Course 2 3-5 Multiplying and Dividing Integers Mr. Reid kept track of his blood sugar daily. He recorded the change each day. What was the average change per day? (–8) + 2 + 4 + (–9) + 6 = –5 Find the sum of the changes in blood sugar. –5 5 = –1 The average change per day was –1 unit. Divide to find the average. Day MonTueWedThuFri Unit Change –824–96

21. Lesson Quiz Find each product or quotient. 1. –8 · 12 2. –3 · 5 · (–2) 3. –75 ÷ 5 4. –110 ÷ (–2) 5. The temperature at Bar Harbor, Maine, was –3°F. It then dropped during the night to be 4 times as cold. What was the temperature then? –96 Insert Lesson Title Here –15 55 Course 2 3-5 Multiplying and Dividing Integers 30 –12˚F