Multiply and rational numbers

ObjectiveThe student will be able to:

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 45

2) Write both numbers as a fraction.

Cross-cancel if possible.

201

45

805

= -16

Multiplying fractions:

top # • top #

Bottom # • bottom#

-24xy

When multiplying two negative numbers, the product is negative.

1. True2. False

Answer Now

When multiplying a negative number and a positive number, use the sign of

the larger number.1. True2. False

Answer Now

25

58

3)

1040

=

14

=

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

Answer 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) 12

6 5 2

5

2

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

Write all numbers as fractions and multiply.

=12

12

61

51

25

21

12010

What is the sign of the product of (-3)(-4)(-5)(0)(-1)(-6)(-91)?

1. Positive2. Negative3. Zero4. Huh?

Answer Now

Dividing Rules

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 Now

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

larger number.1. True2. False

Answer Now

The reciprocal of is

where a and b 0.

ab

ba

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

72

.27

The reciprocal of is

27

72

11

1

Example #2The reciprocal of -3 is

13

.11

131

13

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 1

Answer Now

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

Examples1)

34

58

34

85

65

2420

2) 15

3

10

15

103

1015

23

What is the quotient of-21 ÷ -3?

1. 182. -183. 74. -7

Answer Now

1 10 ?5 3

Answer Now

23

233

503

50

1. .

2. .

3. .

4. .