Multiplying and Dividing Fractions

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Multiplying and Dividing Fractions
Section 4.3
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Multiplying Fractions
of
is
0
1
The word of means multiplication and is means
equal to.
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means
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Multiplying Two Fractions
If a, b, c, and d are numbers and b and d are not
0, then
In other words, to multiply two fractions,
multiply the numerators and multiply the
denominators.
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Examples
If the numerators have common factors with the
denominators, divide out common factors before
multiplying.
1
or
2
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Examples
or
2
1
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Helpful Hint
Recall that when the denominator of a fraction
contains a variable, such as
we assume that the variable is not 0.
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Evaluating Expressions with Fractional Bases
The base of an exponential expression can also be
a fraction.
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Reciprocal of a Fraction
Two numbers are reciprocals of each other if
their product is 1. The reciprocal of the
fraction
is
because
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Dividing Two Fractions
If b, c, and d are not 0, then
In other words, to divide fractions, multiply the
first fraction by the reciprocal of the second
fraction.
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Helpful Hint
Every number has a reciprocal except 0. The
number 0 has no reciprocal. Why?
There is no number that when multiplied by 0
gives the result 1.
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Helpful Hint
When dividing by a fraction, do not look for
common factors to divide out until you rewrite
the division as multiplication.
Do not try to divide out these two 2s.
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Multiplying and Dividing with Fractional
Replacement Values
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