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Multiplying and Dividing Integers Course 2

Learn how to multiply and divide integers through repeated addition and inverse operations. Discover the rules and patterns for multiplication and division of integers, and practice with examples and exercises.

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Multiplying and Dividing Integers Course 2

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

  2. 3-5 Multiplying and Dividing Integers Course 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 17,000 55 28

  3. 3-5 Multiplying and Dividing Integers Course 2 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

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

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

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

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

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

  9. 3-5 Multiplying and Dividing Integers Course 2 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. 3-5 Multiplying and Dividing Integers Course 2 Additional Example 2: Multiplying Integers Multiply. –6 · (–5) Both signs are negative, so the product is positive. –6 · (–5) = 30

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

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

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

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

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

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

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

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

  19. 3-5 Multiplying and Dividing Integers Course 2 Additional Example 4: Averaging Integers 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? Find the sum of the changes in price. (–1) + 3 + 2 + (–5) + 6 = 5 5 5 = 1 Divide to find the average. The average change per day was $1.

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

  21. 3-5 Multiplying and Dividing Integers Course 2 Insert Lesson Title Here 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 30 –15 55 –12˚F

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