3-5 Multiplying and Dividing Integers

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpEvaluate each expression.

1. 17 · 5

2. 8 · 34

3. 4 · 86

4. 20 · 850

5. 275 ÷ 5

6. 112 ÷ 4

85272

344

Course 2

3-5 Multiplying and Dividing Integers

17,000

55

28

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

Learn to multiply and divide integers.

Course 2

3-5 Multiplying and Dividing Integers

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

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.

Try This: Example 1

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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.

Course 2

3-5 Multiplying and Dividing Integers

The Commutative Property of Multiplication states that order does not matter when you multiply.

Remember!

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

Multiply.

Additional Example 2: Multiplying Integers

Course 2

3-5 Multiplying and Dividing Integers

–6 · (–5)

–6 · (–5) = 30 Both signs are negative, sothe product is positive.

Try This: Example 2

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Course 2

3-5 Multiplying and Dividing Integers

Multiply.

–2 · (–8)

–2 · (–8) = 16 Both signs are negative, sothe product is positive.

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.

Course 2

3-5 Multiplying and Dividing Integers

Same signs Positive

Different signs Negative

The rule for division is like the rule for multiplication.

4 • (–2) = –8

–4 • (–2) = 8

–8 ÷ (–2) = 4

8 ÷ (–2) = –4

Course 2

3-5 Multiplying and Dividing Integers

MULTIPLYING AND DIVIDING INTEGERSMULTIPLYING AND DIVIDING INTEGERS

If the signs are: Your answer will be:

the same

different

positive

negative

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.

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.

Try This: Example 1A & 1B

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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.

Try This: Example 3C

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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.

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 Mon Tue Wed Thu Fri

Price Change ($) –$1 $3 $2 –$5 $6

(–1) + 3 + 2 + (–5) + 6 = 5 Find the sum of thechanges in price.

55 = 1

The average change per day was $1.

Divide to find the average.

Try This: Example 4

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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 = –5Find the sum of thechanges in blood sugar.

–55 = –1

The average change per day was –1 unit.

Divide to find the average.

Day Mon Tue Wed Thu Fri

Unit Change –8 2 4 –9 6

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