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Multiplying and Dividing Integers

Review

Multiply or divide.

1. 5(8)

40

72

2. 6(12)

7

4

3.

4.

12

126

5. 18(7)

6.

Learn to multiply and divide integers.

A positive number multiplied by an integer can be

written as repeated addition.

3(200) 200 (200) (200) 600

From what you know about adding and subtracting

integers, you can see that a positive integer

times a negative integer is negative.

You know that multiplying two positive integers

together gives you a positive answer. Look for a

pattern in the integer multiplication at right to

understand the rules for multiplying two negative

integers.

600

200

400

200

200

200

0

The product of two negative integers is a

positive integer.

200

400

600

MULTIPLYING AND DIVIDING TWO INTEGERS

If the signs are the same, the sign of the answer is positive. If the signs are different, the sign of the answer is negative.

Example Multiplying and Dividing Integers

Multiply or divide.

A. 6(4)

Signs are different.

Answer is negative.

24

Signs are the same.

B. 8(5)

Answer is positive.

40

Example Multiplying and Dividing Integers

Multiply or divide.

C.

Signs are different.

Answer is negative.

9

D.

Signs are the same

Answer is positive.

5

Try This

Multiply or divide.

A. 5(2)

Signs are different.

Answer is negative.

10

Signs are the same.

B. 3(2)

Answer is positive.

6

Try This

Multiply or divide.

C.

Signs are different.

Answer is negative.

8

D.

Signs are the same

Answer is positive.

6

(No Transcript)

Example Using the Order of Operations with

Integers

Simplify.

A. 3(6 12)

Subtract inside the parentheses.

3(18)

Think The signs are different.

54

The answer is negative.

B. 5(5 2)

Subtract inside the parentheses.

5(3)

Think The signs are the same.

15

The answer is positive

Example Using the Order of Operations with

Integers

Simplify.

C. 2(14 5)

Subtract inside the parentheses.

2(9)

Think The signs are different.

18

The answer is negative.

Try This

Simplify.

A. 2(1 8)

Subtract inside the parentheses.

2(7)

Think The signs are different.

14

The answer is negative.

B. 4(3 8)

Subtract inside the parentheses.

4(11)

Think The signs are different.

44

The answer is negative.

Try This

Simplify.

C. 3(6 9)

Subtract inside the parentheses.

3(3)

Think The signs are the same.

9

The answer is positive.

The order of operations can be used to find

ordered pair solutions of integer equations.

Substitute an integer value for one variable to

find the value of the other variable in the

ordered pair.

Example 3 Plotting Integer Solutions of Equations

Complete a table of solutions for y 3x 1 for

x 2, 1, 0, 1, and 2. Plot the points on a

coordinate plane.

y

10 8 6 4 2 ?2 ?4 ?6 ?8

10

x 3x 1 y (x, y)

2

1

0

1

2

7

3(2) 1

(2, 7)

x

4

(1, 4)

3(1) 1

?10 ?8 ?6 ?4 ?2 2 4 6 8 10

1

3(0) 1

(0, 1)

3(1) 1

(1, 2)

2

3(2) 1

(2, 5)

5

Try This

Complete a table of solutions for y 2x 3 for

x 2, 1, 0, 1, and 2. Plot the points on a

coordinate plane.

y

10 8 6 4 2 ?2 ?4 ?6 ?8

10

x 2x 3 y (x, y)

2

1

0

1

2

7

2(2) 3

(2, 7)

x

5

(1, 5)

2(1) 3

?10 ?8 ?6 ?4 ?2 2 4 6 8 10

3

2(0) 3

(0, 3)

2(1) 3

1

(1, 1)

2(2) 3

(2, 1)

1

Lesson Quiz Part 1

Perform the given operations.

1. 8(4)

32

2.

6

Evaluate the expressions for the given value of

the variable.

3. 4t 9 for t 6

15

4. for t 9

4

Lesson Quiz Part 2

5. Complete a table of solutions for y 4x 1

for x 3, 1, 1, and 3.

x 4x 1 y (x, y)

3

1

1

3

11

4(3) 1

(3, 11)

3

(1, 3)

4(1) 1

4(1) 1

(1, 5)

5

4(3) 1

(3, 13)

13

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