Transcript Multiplying Fractions PPT

Multiplying Rational
Numbers
(Multiplying Fractions)
DART statement:
I can multiply fractions
(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




 5 4  1 4
4
1
Mixed Numbers
• Convert to improper fractions.
• Simplify.
• Multiply straight across.
Mixed Numbers
• Try these on your own.
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) 

 10  6  60 3 20
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