Math 64
4.3 "Multiplying and Dividing Fractions"
Bibiana Lopez
Riverside City College
June 2010
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Objectives:
* Multiply and divide Fractions.
* Evaluate exponential expressions with fractional bases.
* Multiply and divide given fractional replacement values.
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Multiplying Fractions
Multiplying Fractions
To multiply two fractions, multiply the numerator and multiply
the denominator. If a, b, c, and d represent numbers, and b
a c
a c
=
and d are not 0, we have
b d
b d
Example 1: (Multiplying fractions)
Multiply.
4 3
6
a)
b)
27 8
77
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7
8
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Multiplying Fractions
c)
2
3
3y
2
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d)
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a3 b
b 2 a2
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Evaluating Expressions with Fractional Bases
The base of an exponential expression can also be a fraction.
Example 2: (Evaluating expressions with fractional bases)
Evaluate.
a)
3
2
3
b)
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4
5
2
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Dividing Fractions
Before we can divide fractions, we need to know how to …nd the
reciprocal of a fraction.
Reciprocal of a Fraction
Two numbers are reciprocals of each other if their product is 1. The
a
b
reciprocal of the fraction is because a b = a b = 1
b
a
b a
b a
Multiplying Fractions
To divide two fractions, multiply the …rst fraction by the reciprocal of
the second fraction. If a, b, c, and d represent numbers, and b, c,
a
c
a d
a d
and d are not 0, then
=
=
b d
b c
b c
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Dividing Fractions
Example 3: (Dividing fractions)
Divide. Write all quotients in simplest form.
8 2
3y
a)
b)
7 9
4
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5y 3
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Dividing Fractions
c) 15c 3
3c 2
5
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d)
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5
8
4
7
5
16
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Multiplying & Dividing with Fractional
Recall that two fractions are equivalent if they represent the same
part of a whole. One way to determine whether two fractions are
equivalent is to see whether they simplify to the same fraction.
Example 4: (Multiplying and dividing with fractional replacement values)
If x = 34 and y = 92 , evaluate (a) xy and (b) x y
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Multiplying & Dividing with Fractional
Example 5: (Determining solutions of equations)
Determine whether the given replacement values are solutions of the given
equations.
5
3
1
5
a solution to 3x =
b) Is
a solution to 5x =
a) Is
18
6
5
3
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