11-7 Dividing Integers

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpFind each quotient.

1. 18 ÷ 2 2. 42 ÷ 7

3. 56 ÷ 8 4. 24 ÷ 6

5. 3,600 ÷ 4 6. 540 ÷ 60

9 6

7

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11-7 Dividing Integers

4

900 9

Problem of the Day

Hank wanted to record the number of marbles he lost to his friend Marcus each day for 5 days. He forgot to record one day, but for the other days he wrote 8, 2, 3, and 4. The average number he lost was 4. What number did he forget to write?3

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11-7 Dividing Integers

Learn to divide integers.

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11-7 Dividing Integers

Multiplication and division are inverse operations. To solve a division problem, think of the related multiplication.

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11-7 Dividing Integers

To find the mean of a list of numbers:

1. Add all the numbers together.

2. Divide by how many numbers are in the list.

Remember!

Additional Example 1: Dividing Integers

Find each quotient.

A. –30 ÷ 6

B. –42 ÷ (–7)

Think: What number times 6 equals –30?

–5 • 6 = –30, so –30 ÷ 6 = –5.

Think: What number times –7 equals –42?

6 • (–7) = –42, so –42 ÷ (–7) = 6.

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11-7 Dividing Integers

Check It Out: Example 1

Find each quotient.

A. –15 ÷ 5

B. –36 ÷ (–6)

Think: What number times 5 equals –15?

–3 • 5 = –15, so –15 ÷ 5 = –3.

Think: What number times -6 equals –36?

6 • (–6) = –36, so –36 ÷ (–6) = 6.

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11-7 Dividing Integers

Dividing IntegersIf the signs are the same, the product is positive.

24 ÷ 3 = 8 –6 ÷ (–3) = 2

If the signs are different, the quotient is negative.

–20 ÷ 5 = –4 72 ÷ (–8) = –9

Zero divided by any integer equals 0.

= 0 = 0014__ 0

–11 __

You cannot divide any integer by 0.

Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers.

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11-7 Dividing Integers

Additional Example 2A: Evaluating Integer Expressions

Evaluate for each value of d.

d = 16

Write the expression.

= 16 ÷ 4 Substitute 16 for d.

= 4 The signs are the same, so the answer is positive.

d 4__

d 4__

16 4 __

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11-7 Dividing Integers

Additional Example 2B: Evaluating Integer Expressions

Evaluate for each value of d.

d = –24

Write the expression.

= –24 ÷ 4 Substitute –24 for d.

= –6 The signs are different, so the answer is negative.

d 4__

d 4__

-24 4 ___

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11-7 Dividing Integers

Additional Example 2C: Evaluating Integer Expressions

Evaluate for each value of d.

d = –12

Write the expression.

= –12 ÷ 4 Substitute –12 for d.

= –3 The signs are different, so the answer is negative.

d 4__

d 4__

-12 4 ___

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11-7 Dividing Integers

Check It Out: Example 2A

Evaluate for each value of c.

c = –15

Write the expression.

= –15 ÷ 3 Substitute –15 for c.

= –5 The signs are different, so the answer is negative.

c 3__

c 3__

-15 3 ___

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11-7 Dividing Integers

Check It Out: Example 2B

Evaluate for each value of c.

c = 12

Write the expression.

= 12 ÷ 3 Substitute 12 for c.

= 4

c 3__

c 3__

12 3 ___

The signs are the same, so the answer is positive.

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11-7 Dividing Integers

Check It Out: Example 2C

Evaluate for each value of c.

c = 27

Write the expression.

= 27 ÷ 3 Substitute 27 for c.

= 9 The signs are the same, so the answer is positive.

c 3__

c 3__

27 3 __

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11-7 Dividing Integers

Lesson QuizFind each quotient.

1. 18 ÷ (–3) 2. –36 ÷ (–6)

3. –64 ÷ (–8) 4. –45 ÷ 3

Evaluate for each value of x.

5. x = –12 6. x = 20

7. Carmen’s mom has $3,200 in her bank

account. If she uses the money to make

monthly rent payments of $375, how many

whole payments can she make?

6–6

Insert Lesson Title Here

8 –15

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11-7 Dividing Integers

–3 5

8

x 4__