Rational Numbers mulplying and etccc.ppt

This is a presentation about rational number, credits to the real owner of this.

1. Chapter 7Chapter 7
Section 2Section 2
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Multiplying and Dividing Rational
Expressions
Multiply rational expressions.
Divide rational expressions.
1
2
7.27.2

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 11
Multiply rational expressions.
Slide 7.2 - 3

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Multiply rational expressions.
The product of two fractions is found by multiplying the
numerators and multiplying the denominators. Rational
expressions are multiplied in the same way.
The product of the rational expressions and is

That is, to multiply rational expressions, multiply the numerators
and multiply the denominators.
Slide 7.2 - 4
P
Q
R
S
P R PR
Q S QS
 

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 1
Multiply. Write each answer in lowest terms.
Solution:
Multiplying Rational
Expressions
Slide 7.2 - 5
2 5
7 10

2
2
8 9
3
p q
pq

2 5
7 10



2
2
8 9
3
p q
p q
  

 
7
2 5
2 5


 
1
7

38
3
3p qp
p qq
    

  
24p
q

It is also possible to divide out common factors in the numerator
and denominator before multiplying the rational expressions.

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Multiply. Write the answer in lowest terms.
EXAMPLE 2
Solution:
Multiplying Rational
Expressions
Slide 7.2 - 6


3
2
p q q
p p q





3
2
p q q
p q p
  

  


3
2
q
qp
p q
p
 


 3
2
q
p


7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 3
Multiply. Write the answer in lowest terms.
  
  
2
2
7 10 6 6
3 6 2 15
x x x
x x x
  

  
Solution:
2
2
7 10 6 6
3 6 2 15
x x x
x x x
  

  
Deciding whether Ordered Pairs
Are Solutions of an Equation
Slide 7.2 - 7


2 13 2
3 5 3
5
2
x x x
xx x
 
 



 

2 1
3
x
x



 
 
2 6 6
3 3
5
56
x x
x
x
x x


 

 

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 22
Divide rational expressions.
Slide 7.2 - 8

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Divide rational expressions.
Division of rational expressions is defined as follows.
If and are any two rational expressions with
then

That is, to divide one rational expression by another rational
expression, multiply the first rational expression by the reciprocal
of the second rational expression.
Slide 7.2 - 9
.
P R P S PS
Q S Q R QR
   
,0
R
S

R
S
P
Q

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 4
Solution:
2 9.y x 
4
3 44
5
 


3 16
4 5
 
12
5

3
2
3
3
p p
ppp


 
 
 
3 5
4 16

2
3
3 4
3 4
9
6
p p
p p
 


Dividing Rational Expressions
Slide 7.2 - 10
Divide. Write each answer in lowest terms.
2 3
9 6
3 4 3 4
p p
p p

 
3
2p


11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 5
Divide. Write the answer in lowest terms.
Solution:
2 2
5 10
2 8
a b ab

Dividing Rational Expressions
Slide 7.2 - 11
2
2
5 8
2 10
a b
ab
 
5 2 2
2 2 5
2a b
a
a
bb
    

    
2a
b


12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Divide. Write the answer in lowest terms.
EXAMPLE 6
Dividing Rational Expressions
Slide 7.2 - 12
 
2
2
4 3 3
2 1 4 1
x x x x
x x
  

 


2
2
4 4
1
3
2 3
1xx x
x x x

 
 


  
 
2 1
1
4 2
2
1
1
x x
xx
x
x
 

  

 4 2 1x
x


Solution:

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 7
2
2 2
1 2 1
ab a a b
a a a
 

  
Dividing Rational Expressions
(Factors Are Opposites)
Slide 7.2 - 13
Divide. Write in the answer in lowest terms.
Solution:


1 1
1
1
1
a aa b a
a ba a
 


 
 
2 2
2
2 1
1
ab a a a
a a b
  
 
 


1
1
a a
a



Remember to write −1 when dividing out factors that are opposite of
each other. It may be written in the numerator or denominator, but not
both.

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Multiplying or Dividing Rational Expressions.
Slide 7.2 - 14
In summary, use the following steps to multiply or divide
rational expressions.
Step 1: Note the operation. If the operation is division, use
the definition of division to rewrite it as multiplication.
Step 2: Multiply numerators and denominators.
Step 3: Factor all numerators and denominators completely.
Step 4: Write in lowest terms using the fundamental property.
Steps 2 and 3 may be interchanged based on personal
preference.