CONFIDENTIAL 1 Multiplying and Dividing Real Numbers Multiplying and Dividing Real Numbers.

CONFIDENTIAL 1

Multiplying Multiplying and Dividingand Dividing

Real NumbersReal Numbers

CONFIDENTIAL 2

Warm UpWarm Up

1) 12 - 18

2) -6 + 14

3) 3 - (-5)

4) 11 + (-8)

Add or subtract:

CONFIDENTIAL 3

Multiplying and Dividing Real NumbersMultiplying and Dividing Real Numbers

When you multiply two numbers, the signs of the numbers you are multiplying determine whether the product is

positive or negative.

This is true for division also.

CONFIDENTIAL 4

Multiplying and Dividing Signed Multiplying and Dividing Signed NumbersNumbers

CONFIDENTIAL 5

B) 8x for x = -5 4

8x = 8 x -5 4= 8(-5) 4= -40 = -10 4

First substitute - 5 for x. 4

Multiply.

The quotient of two numbers with different signs is negative.

Multiplying and Dividing Signed NumbersMultiplying and Dividing Signed Numbers

Find the value of each expression.

A) -12 · 5 = -60

The product of two numbers with different signs is negative.

CONFIDENTIAL 6


Now you try!

1a) 35 ÷ (-5)

1b) -11 (-4)

1c) -6x for x = 7

CONFIDENTIAL 7

Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses . To divide by a number, you can multiply

by its multiplicative inverse.

Dividing by a nonzero number is the same as multiplying by the reciprocal of the number.

CONFIDENTIAL 8

Dividing by FractionsDividing by Fractions

Divide.

To divide by - 8 , multiply by -15 . 15 8Multiply the numerators and multiplythe denominators.

- 4 , multiply by -8 have the same sign, 5 15so the quotient is positive.

CONFIDENTIAL 9

Write 4 as a fraction with a denominatorof 1. Write 1 as an improper fraction. 4

To divide by 37 , multiply by 4 . 4 37

- 4 and 1 have different signs, 4so the quotient is negative.

9

9

CONFIDENTIAL 10

Divide.

Now you try!

2a)

2b)

2c)

CONFIDENTIAL 11

No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal.

Because of this, division by 0 is not possible. We say that division by 0 is undefined.

CONFIDENTIAL 12

Properties of ZeroProperties of Zero

CONFIDENTIAL 13

Multiplying and Dividing with ZeroMultiplying and Dividing with Zero

A) 0 ÷ 16.568 = 0

B) 63 7 ÷ 0 8 = undefined

C) 1 · 0 = 0

Multiply or divide if possible.

Zero is divided by a nonzero number.The quotient of zero and any nonzero number is 0.

A number is divided by zero.

Division by zero is undefined.

A number is multiplied by zero.The product of any number and 0 is 0.

CONFIDENTIAL 14

Multiply or divide.

Now you try!

3a)

3b)

3c)

CONFIDENTIAL 15

Recreation ApplicationRecreation Application

A hot-air balloon is taken for a 2.5-hour trip. The wind speed (and the speed of the balloon) is 4.75 mi/h. The balloon travels

in a straight line. How many miles away from the liftoffsite will the balloon land?

Find the distance traveled at a rate of 4.75 mi/h for 2.5 hours. To find distance, multiply rate by time.

rate times time4.75 · 2.5= 11.875

The hot-air balloon will land 11.875 miles from the liftoff site.

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4) On another hot-air balloon trip, the wind speed is 5.25 mi/h. The trip is planned for 1.5 hours. The balloon travels in a straight line. How many miles

away from the liftoff site will the balloon land?

Now you try!

CONFIDENTIAL 17

Assessment


1) -72 ÷ (-9)

2) 11 (-11) 3) -7.2 ÷ x for x = 3.6

CONFIDENTIAL 18

Divide:

4)

5)

6)

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7) 3.8 ÷ 0

8) 0 (-27)

9) 0 ÷ 2 3

CONFIDENTIAL 20

10) It is estimated that 7 million people saw off-Broadway shows in 2002. Assume that the average price of a ticket was $30. How much money was spent on tickets for off-

Broadway shows in 2002?

CONFIDENTIAL 21

Multiplying and Dividing Real NumbersMultiplying and Dividing Real Numbers

When you multiply two numbers, the signs of the numbers you are multiplying determine whether the product is

positive or negative.

This is true for division also.

Let’s review

CONFIDENTIAL 22

Multiplying and Dividing Signed Multiplying and Dividing Signed NumbersNumbers

CONFIDENTIAL 23

B) 8x for x = -5 4

8x = 8 x -5 4= 8(-5) 4= -40 = -10 4

First substitute - 5 for x. 4

Multiply.

The quotient of two numbers with different signs is negative.

Multiplying and Dividing Signed NumbersMultiplying and Dividing Signed Numbers


A) -12 · 5 = -60

The product of two numbers with different signs is negative.

CONFIDENTIAL 24

Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses . To divide by a number, you can multiply

by its multiplicative inverse.

Dividing by a nonzero number is the same as multiplying by the reciprocal of the number.

CONFIDENTIAL 25

Dividing by FractionsDividing by Fractions

Divide.

To divide by - 8 , multiply by -15 . 15 8Multiply the numerators and multiplythe denominators.

- 4 , multiply by -8 have the same sign, 5 15so the quotient is positive.

CONFIDENTIAL 26

Properties of ZeroProperties of Zero

CONFIDENTIAL 27

Multiplying and Dividing with ZeroMultiplying and Dividing with Zero

A) 0 ÷ 16.568 = 0

B) 63 7 ÷ 0 8 = undefined

C) 1 · 0 = 0


Zero is divided by a nonzero number.The quotient of zero and any nonzero number is 0.

A number is divided by zero.

Division by zero is undefined.

A number is multiplied by zero.The product of any number and 0 is 0.

CONFIDENTIAL 28

Recreation ApplicationRecreation Application

A hot-air balloon is taken for a 2.5-hour trip. The wind speed (and the speed of the balloon) is 4.75 mi/h. The balloon travels

in a straight line. How many miles away from the liftoffsite will the balloon land?

Find the distance traveled at a rate of 4.75 mi/h for 2.5 hours. To find distance, multiply rate by time.

rate times time4.75 · 2.5= 11.875

The hot-air balloon will land 11.875 miles from the liftoff site.

CONFIDENTIAL 29

You did a great job You did a great job today!today!

CONFIDENTIAL 1 Multiplying and Dividing Real Numbers Multiplying and Dividing Real Numbers.

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