Transcript Multiply and Divide Fractions

Multiplying and
Dividing Rational
Numbers
Rational Numbers
• The term Rational Numbers refers to any number that can
be written as a fraction.
• This includes fractions that are reduced, fractions that can
be reduced, mixed numbers, improper fractions, and even
integers and whole numbers.
• An integer, like 4, can be written as a fraction by putting the
number 1 under it.
4
4
1
Multiplying Fractions
• When multiplying fractions, they do NOT need to
have a common denominator.
• To multiply two (or more) fractions, multiply across,
numerator by numerator and denominator by
denominator.
• If the answer can be simplified, then simplify it.
• Example: 2  9  2  9  18 2  9
5 2
52
10 2
• Example: 3  5  3 5  15
4 2
4 2
8
5
Simplifying Diagonally
• When multiplying fractions, we can simplify the
fractions and also simplify diagonally. This isn’t
necessary, but it can make the numbers smaller and
keep you from simplifying at the end.
• From the last slide: 2  9  2  9  18 2  9
5 2
52
1
10 2
5
• An alternative: 2  9  1 9  9
5 2
1
5 1
5
You do not have to simplify diagonally, it is just an option. If you
are more comfortable, multiply across and simplify at the end.
Mixed Numbers
• To multiply mixed numbers, convert them to
improper fractions first.
3 2 1 1   35  2 1 4  1  175 
 5  4   5  4   5 4 
1
175  17 1 17


   
1 4
4
5 4
1
Sign Rules
• Remember, when multiplying signed numbers...
Positive * Positive = Positive.
Negative * Negative = Positive.
Positive * Negative = Negative.
3
6 2
3  2 

1)    
20
40 2
8 5
3  1  3 3 1


2)    
60 3 20
10
6
Try These: Multiply
Multiply the following fractions and mixed numbers:
6  1 
1)  
5 3
1 6
2) 5 
3 5
3  1 

3) 1 3 
4
2
4 6
4)

9 8
Solutions: Multiply
6  1 
6 3
2
1)    

5 3
15 3
5
1 6 16 6 96 3 32
2) 5    

3 5 3 5 15 3 5
3  1   7 7 49

3) 1 3      
4
2
4
2
8
4 6 24 24 1
4)
 

9 8 72 24 3
Solutions (alternative): Multiply
Note: Problems 1, 2 and 4 could have been simplified before
multiplying.
2
2
6  1 
1)    
5
5 3
1
2
1 6 16 6
32
2) 5   

3 5 13 5
5
1
3
4 6
1 6
1 3
4)

 
 
9 82 9 21
9 1
3
1
1

3
Dividing Fractions
• When dividing fractions, they do NOT need to have a
common denominator.
• To divide two fractions, change the operation to
multiply and take the reciprocal of the second fraction
(flip the second fraction). Keep-Change-Flip.
Change Operation.
2 9 2 2
  
5 2 5 9
Flip 2nd Fraction.
Dividing Fractions
• Finish the problem by following the rules for
multiplying fractions.
2 9 2 2
4
   
5 2 5 9 45
Try These: Divide
• Divide the following fractions & mixed numbers:
6  1 
1)   
5
2
3  1 
2)    
2
2
1
2
3) 2  3
3
3
7
2
4)   1
3
3
Solutions: Divide
6  1  6  2 
12
1)
        
5
2
5
1
5
3  1 
3  2  6 2 3
2)          
 3
2
2
2
1
2 2 1
1
2 7 11 7 3 21 3 7
3) 2  3     

3
3 3 3 3 11 33 3 11
7
2
7 5
7 3
21 3
7
4)   1        

3
3
3 3
3 5
15 3
5