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Chapter 2
Multiplying and
Dividing Fractions
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
2.4
Multiplying Fractions and
Mixed Numbers
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Fractions
Multiplying Fractions
To multiply two fractions, multiply the numerators and
multiply the denominators.
If a, b, c, and d represent positive whole numbers we
have
a c a c
 
b d bd
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Examples
Multiply.
a. 2  3  2  3  6
7 5
75
35
1 1  1
1 1
 
b.
33
11 3 11  3
c.
8
2 4


21
3 7
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Examples
Multiply and simplify.
a. 3  8  3  2  2  2  6
4 11
2  2 11
11
2  3 2  7
1
2 3 14


b.  
7  2  2  2  3  5 10
7 8 15
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Multiplying Fractions and Mixed Numbers or
Whole Numbers
Multiplying Fractions and Mixed Numbers of
Whole Numbers
To multiply with mixed numbers or whole numbers,
first write any mixed or whole numbers as fractions and
then multiply as usual.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Examples
Multiply.
8 7
2227
7
1
2 7
 or 2
a. 2    
3
3 8
3 2  2  2
3
3 8
b.
2  43
43
7
2 3 2 43


1
5  
36
36
9 8 9 8 3 3 2  2  2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Example
Multiply.
5 27
7
35
3
10  

or 8
8 1 2  2  2
4
4
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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Example
Multiply. Check by estimating.
20 5
2 1
5 2 25
2 1  

9 4
9 4
3 3 2  2
25
7

or 2
9
9
Let’s check by estimating.
2
1
2 rounds to 2, 1 rounds to 1, and 2 · 1 = 2.
9
4
The estimate is close to the exact value, so our
answer is reasonable.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
9
Example
1
An estimate for the measure of an adult’s wrist is
4
of the waist size. If Jorge has a 34-inch waist,
estimate the size of his wrist.
34 1 17  2 1 17 or 8 1
 

2
1 4 1 2  2
2
1
Jorge’s wrist is about 8 inches.
2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Basic Mathematics, 4e
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