2.7 Division of Real Numbers
GOAL
1
DIVIDING 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
1
a
 a , a n d the reciprocal of
a
b

b
.
a
Since 0 does not have a reciprocal, we cannot divide by 0.
DIVISION RULE
To divide a number a by a nonzero number b, multiply a by
the reciprocal of b.
1
ab a
b
EXAMPLE 1
Extra Example 1
Find each quotient.
a. 1 5    5 
b.
 1
15    
 5
c.
2
45 
45 
6
6
3
5
54
1
1
3
3
d.
2
7  1
 
3  3
3
3
1
2
7


5
9
3
2
2.7 Division of Real Numbers
GOAL
2
WORKING WITH ALGEBRAIC EXPRESSIONS
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 _______.
positive
negative
•If the signs are different, the product is ________.
EXAMPLE 2
Extra Example 2
Simplify the expression:
Multiply by the reciprocal.
9  27 x
3
.
 1
9  27 x    
 3
 1
 1
Use the distributive property. 9     2 7 x   
 3
 3
Simplify.
EXAMPLE 3
3  9 x
Extra Example 3
Evaluate the expression when x = –5 and y = –1.
a.
x y
y 1
b.
2y
x 1
c.
5x
5
 5    1
2   1
5   5 
1  1
5  1
5
6
2
0
0
6
5
Undefined
1
3
0
Checkpoint
1. Simplify the expression
2. Evaluate the expression
25d  125
5
s  3t
.
–5d + 25
when s = –3 and t = –1.
2s
0
EXAMPLE 4
Extra Example 4
A mountain climber descends 300 feet in 50 minutes. What
is her velocity?
–300 feet
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
SOLVE
Displacement
Velocity =
Time
v
v 
50 min
 3 0 0 ft
5 0 m in
v  6
ft
m in
EXAMPLE 5
Extra Example 5
Find the domain of the function y 
2x
.
4x
Since 4x cannot equal 0, the domain is
all real numbers except x = 0.
Checkpoint
1. An elevator descends 120 feet in 1.5 minutes. What is
its velocity?
6
ft
m in
2. Find the domain of the function y 
6
4 x
.
All real numbers except x = –4.
QUESTIONS?