Lesson 2-6 and 2-7 Multiplying and Dividing

Rational Numbers

ObjectiveStudents will be able to:1.multiply rational numbers2.divide rational numbers

Multiplying Rules

1) If the numbers have the same signs then the product is positive.

(-7) • (-4) = 282) If the numbers have

different signs then the product is negative.

(-7) • 4 = -28

Examples

1) (3x)(-8y)

20 4

5

2) Write both numbers as a fraction.

Cross-cancel if possible.

20

1

4

5

80

5= -16

Multiplying fractions:

top # • top #

Bottom # • bottom#

-24xy

When multiplying two negative numbers, the

product is negative.1. True2. False

Answer NowAnswer Now

When multiplying a negative number and a positive number,

use the sign of the larger number.1. True2. False

Answer NowAnswer Now

2

5

5

8

3)

10

40=

1

4=

Multiply: (-3)(4)(-2)(-3)1. 722. -723. 364. -36

Answer NowAnswer Now

an easy way to determine the sign of the answer

3 negative signs -> Odd -> answer is negative-480

When you have an odd number of negatives, the answer is negative.

When you have an even number of negatives, the answer is positive.

4) (-2)(-8)(3)(-10)Do you have an even or odd number of

negative signs?

Last one!

5) 1

2

6 5 2

5

2

Positive or negative answer?Positive - even # of negative signs (4)

Write all numbers as fractions and multiply.

=12

1

2

6

1

5

1

2

5

2

1

12010

Dividing Rules (same as multiplication)

1) If the numbers have the same signs then the quotient is positive.

-32 ÷ (-8 )= 42) If the numbers have different

signs then the quotient is negative.

81 ÷ (-9) = -9

When dividing two negative numbers, the quotient is

positive.1. True2. False

Answer NowAnswer Now

When dividing a negative number and a positive number, use the

sign of the larger number.1. True2. False

Answer NowAnswer Now

The reciprocal of is

where a and b 0.

a

b

b

a

The reciprocal of a number is called its multiplicative inverse.

A number multiplied by its reciprocal/multiplicative inverse is

ALWAYS equal to 1.

Example #1

7

2.

2

7The reciprocal of is

2

7

7

2 1

11

Example #2

The reciprocal of -3 is

1

3.

1

11

3

1

1

3

Basically, you are flipping the fraction!

We will use the multiplicative inverses

for dividing fractions.

Which statement is false about reciprocals?

1. Reciprocals are also called additive inverses

2. A number and its reciprocal have same signs

3. If you flip a number, you get the reciprocal

4. The product of a number and its reciprocal is 1Answer NowAnswer Now

When dividing fractions, change division to multiplying by the reciprocal.

Examples

1) 3

4

5

8

3

4

8

5

6

5

24

20

2) 1

5

3

10

1

5

10

3

10

15

2

3

What is the quotient of-21 ÷ -3?

1. 182. -183. 74. -7

Answer NowAnswer Now

1. .

2. .

3. .

4. .

1 10?

5 3

Answer NowAnswer Now

2

3

2

33

503

50

Homework:

OLesson 2-6 p. 109, 110 # 18-

45 every 3rd

OLesson 2-7 p. 115 # 15 -42

every 3rd