GOAL 1 DIVIDING REAL NUMBERS

2.7 Division of Real Numbers

VOCABULARY

•reciprocal

Since we use reciprocals when dividing, you must be able to write the reciprocal of a number. Remember:

The reciprocal of the reciprocal of 1

, a anda

.a b

b a

Since 0 does not have a reciprocal, we cannot divide by 0.

To divide a number a by a nonzero number b, multiply a by the reciprocal of b.

DIVISION RULE

1a b a

b

EXAMPLE 1

Extra Example 1

Find each quotient.

a. b.

c. d.

15 5 1

155

3

545

6

645

5

54

12

33

7 1

3 3

7

9

123

31

2

3

2

GOAL 2 WORKING WITH ALGEBRAIC EXPRESSIONS

2.7 Division of Real Numbers

EXAMPLE 2

Since we divide by multiplying by the reciprocal, the same rules about signs apply.

Rules for dividing two real numbers:

•If the signs are the same, the product is _______.

•If the signs are different, the product is ________.

positive

negative

Extra Example 2

EXAMPLE 3

Simplify the expression: 9 27.

3

x

Multiply by the reciprocal. 19 27

3x

Use the distributive property.1 1

9 273 3

x

Simplify. 3 9x

Extra Example 3Evaluate the expression when x = –5 and y = –1.

a. b. c.1

x y

y

5 1

1 1

6

0

Undefined

2

1

y

x

2 1

5 1

2

6

1

3

5

5

x

5 5

5

0

5

0

Checkpoint

1. Simplify the expression 25 125.

5

d

–5d + 25

2. Evaluate the expression when s = –3 and t = –1.3

2

s t

s

0

EXAMPLE 4

Extra Example 4A mountain climber descends 300 feet in 50 minutes. What is her velocity?

EXAMPLE 5

VERBAL MODEL

LABELS

ALGEBRAIC MODEL

SOLVE

=VelocityDisplacement

Time

v 50 min

–300 feet

300 ft

50 minv

ft6

minv

Extra Example 5

Find the domain of the function 2

.4

xy

x

Since 4x cannot equal 0, the domain is all real numbers except x = 0.

Checkpoint1. An elevator descends 120 feet in 1.5 minutes. What is its velocity?

2. Find the domain of the function 6

.4

yx

ft6

min

All real numbers except x = –4.

QUESTIONS?