2 4 Multiplying and Dividing Integers Warm Up
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2 -4 Multiplying and Dividing Integers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Objective: Students multiply and divide integers
2 -4 Multiplying and Dividing Integers Warm Up Evaluate each expression. 1. 17 · 5 85 2. 8 · 34 272 3. 4 · 86 344 4. 20 · 850 17, 000 5. 275 ÷ 5 55 6. 112 ÷ 4 28
2 -4 Multiplying and Dividing Integers Problem of the Day 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
2 -4 Multiplying and Dividing Integers Learn to multiply and divide integers.
2 -4 Multiplying and Dividing Integers You can think of multiplication as repeated addition. 3 · 2 = 2 + 2 = 6 and 3 · (– 2) = (– 2) + (– 2) = – 6
2 -4 Multiplying and Dividing Integers Additional Example 1 A: Multiplying Integers Using Repeated Addition Use a number line to find each product. – 7 · 2 = 2 · (-7) Use the Commutative Property. + (– 7) -14 -13 -12 -11 -10 -9 -8 -7 + (– 7) -6 Think: Add -7 two times. – 7 · 2 = – 14 -5 -4 -3 -2 -1 0
2 -4 Multiplying and Dividing Integers Additional Example 1 B: Multiplying Integers Using Repeated Addition Use a number line to find each product. – 8 · 3 = 3 · (– 8) + (– 8) Use the Commutative Property. + (– 8) – 24– 23– 22– 21– 20– 19– 18– 17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 Think: Add – 8 three times. – 8 · 3 = – 24
2 -4 Multiplying and Dividing Integers Check It Out: Example 1 A Use a number line to find each product. – 3 · 2 = 2 · (-3) Use the Commutative Property. + (– 3) -14 -13 -12 -11 -10 -9 -8 -7 -6 Think: Add -3 two times. – 3 · 2 = – 6 -5 -4 + (– 3) -3 -2 -1 0
2 -4 Multiplying and Dividing Integers Check It Out: Example 1 B Use a number line to find each product. – 5 · 3 = 3 · (– 5) + (– 5) Use the Commutative Property. + (– 5) -15 -14 -13 -12 -11 -10 -9 -8 -7 + (– 5) -6 Think: Add – 5 three times. – 5 · 3 = – 15 -5 -4 -3 -2 -1
2 -4 Multiplying and Dividing Integers Remember! Multiplication and division are inverse operations. They “undo” each other. Notice how these operations undo each other in the patterns shown.
2 -4 Multiplying and Dividing Integers The patterns below suggest that when the signs of integers are different, their product or quotient is negative. The patterns also suggest that the product or quotient of two negative integers is positive.
2 -4 Multiplying and Dividing Integers MULTIPLYING AND DIVIDING TWO INTEGERS If the signs are: Your answer will be: the same positive different negative
2 -4 Multiplying and Dividing Integers Additional Example 2: Multiplying Integers Find each product. A. – 6 · (– 5) 30 Both signs are negative, so the product is positive. B. – 4 · 7 -28 The signs are different, so the product is negative.
2 -4 Multiplying and Dividing Integers Check It Out: Example 2 Find each product. A. – 2 · (– 8) 16 Both signs are negative, so the product is positive. B. – 3 · 5 – 15 The signs are different, so the product is negative.
2 -4 Multiplying and Dividing Integers Additional Example 3: Dividing Integers Find each quotient. A. 35 ÷ (– 5) – 7 B. – 32 ÷ (– 8) 4 Think: 35 ÷ 5 = 7. The signs are different, so the quotient is negative. Think: 32 ÷ 8 = 4. The signs are the same, so the quotient is positive.
2 -4 Multiplying and Dividing Integers Additional Example 3: Dividing Integers Find the quotient. C. – 48 ÷ 6 – 8 Think: 48 ÷ 6 = 8. The signs are different, so the quotient is negative.
2 -4 Multiplying and Dividing Integers Check It Out: Example 3 Find each quotient. A. – 12 ÷ 3 – 4 B. 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.
2 -4 Multiplying and Dividing Integers Check It Out: Example 3 Find the quotient. C. – 25 ÷ (– 5) – 25 ÷ – 5 5 Think: 25 ÷ 5 = 5. The signs are the same, so the quotient is positive.
2 -4 Multiplying and Dividing Integers Zero divided by any number is zero, but you cannot find an answer for division by zero. For example – 6 ÷ 0 ≠ 0, because 0 · 0 ≠ – 6. We say that division by zero is undefined.
2 -4 Multiplying and Dividing Integers 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? Mon Tue Day Price Change ($) –$1 $3 (– 1) + 3 + 2 + (– 5) + 6 = 5 5÷ 5=1 Wed $2 Thu Fri –$5 $6 Find the sum of the changes in price. Divide to find the average. The average change was $1 per day.
2 -4 Multiplying and Dividing Integers Check It Out: Example 4 Mr. Reid kept track of his blood sugar daily. He recorded the change each day. What was the average change per day? Day Unit Change Mon – 8 Tue 2 Wed 4 Thu – 9 Fri 6 Find the sum of the changes in blood (– 8) + 2 + 4 + (– 9) + 6 = – 5 sugar. Divide to find the – 5 ÷ 5 = – 1 average. The average change per day was – 1 unit.
2 -4 Multiplying and Dividing Integers Lesson Quizzes Standard Lesson Quiz for Student Response Systems
2 -4 Multiplying and Dividing Integers Lesson Quiz: Part I Use a number line to find the product. 1. – 8 · 2 – 16 Find each product or quotient. 2. – 3 · 5 · (– 2) 3. – 75 ÷ 5 4. – 110 ÷ (– 2) 30 – 15 55
2 -4 Multiplying and Dividing Integers Lesson Quiz: Part II 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? – 12°F
2 -4 Multiplying and Dividing Integers Lesson Quiz for Student Response Systems 1. Identify the number line that helps to find the product. – 7 · 3 A. – 21 B. – 10
2 -4 Multiplying and Dividing Integers Lesson Quiz for Student Response Systems 2. Identify the product. – 4 · 6 · (– 4) A. 96 B. 2 C. – 2 D. – 96
2 -4 Multiplying and Dividing Integers Lesson Quiz for Student Response Systems 3. Identify the quotient. – 66 ÷ 6 A. 10 B. 11 C. – 10 D. – 11
2 -4 Multiplying and Dividing Integers Lesson Quiz for Student Response Systems 4. Identify the quotient. – 122 ÷ (– 2) A. – 62 B. – 61 C. 61 D. 62
2 -4 Multiplying and Dividing Integers Lesson Quiz for Student Response Systems 5. The level of water in a tank is 16 feet. The level decreases steadily, and the tank is emptied in 8 hours. What was the change in water level in the tank during the first hour? A. 3 ft B. 2 ft C. – 2 ft D. – 3 ft
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