MULTIPLICATION: Example 2

Rule 13: To multiply three or more simple fractions, complete the following three steps.

1.

Multiply the numerators.

2.

Multiply the denominators.

3.

Reduce the results. (See Rule 10)
a.
Factor the product of the numerators.
b.
Factor the product of the denominators.
c.
Look for the fractions that have a value of 1.

Example 2: Multiply tex2html_wrap_inline151 and reduce the answer.

Answer. The answer is .

Solution. Multiply the numerators and the denominators, but leave them in factored form tex2html_wrap_inline155 .

You can see several ways to go from the problem. Your observations should include that the factor 12 appears in both the numerator and denominator, the number 10 in the numerator will divide evenly into the number 50 in the denominator, and the number 16 in the denominator will divide evenly into the 32 in the numerator.

Factor the numerator and denominator using these observations. Look for the factors in the mix that have a value equal to 1. We have

The fraction tex2html_wrap_inline159 can be further reduced to

Note: Another way to work the problem is to reduce each fraction first and then complete the above steps.

The fraction can be reduced to
The fraction can be reduced to
The fraction can be reduced to
The fraction can be reduced to
The original problem can now be written
Therefore we have

Check: You can prove the answer with your calculator. Calculate 12 divided by 16, 10 divided by 12, 24 divided by 50, 32 divided by 60, and and multiply the answers. Now calculate 4 divided by 25. If you are correct, the answers are the same (equivalent) and you have successfully completed the problem.

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Author: Nancy Marcus