Download 2.7 Division of Real Numbers

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:
1
a b
 a, and the reciprocal of
 .
The reciprocal of
a
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. 15   5 
 1
15    
 5
3
1
c. 2 3
3
7  1
 
3  3
7

9
b.
d.
5
6
6
45 
5
54
45 
1
2
3
3
1 
2
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
9


27
x
 
Use the distributive property. 


 3
 3
Simplify.
EXAMPLE 3
3  9x
Extra Example 3
Evaluate the expression when x = –5 and y = –1.
xy
a.
y 1
b.
2y
x 1
c.
5x
5
2  1
5   5 
1  1
5  1
5
6
0
2
6
0
5
Undefined
1
3
0
5   1
Checkpoint
1. Simplify the expression
2. Evaluate the expression
25d  125
.
5
–5d + 25
s  3t
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
300 ft
50 min
ft
v  6
min
EXAMPLE 5
Extra Example 5
2 x
.
Find the domain of the function y 
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?
ft
6
min
6
.
2. Find the domain of the function y 
4x
All real numbers except x = –4.
QUESTIONS?