SUBTRACTION: Example 4

Rule 19:
To subtract, the denominators must be equal. You essentially following the same steps as in addition.
1.
Build each fraction so that both denominators are equal.
2.
Combine the numerators according to the operation of subtraction or additions.
3.
The denominators will be the denominator of the built-up fractions.
4.
Reduce the answer.

Example:
Calculate tex2html_wrap_inline48 .
Answer:
The answer is tex2html_wrap_inline50 .
Solution:
The denominators are different; therefore, the first step is to build the fractions to fractions with common denominators. 24 can be factored as follows: 24 = 4 tex2html_wrap_inline52 6 = 2 tex2html_wrap_inline52 2 tex2html_wrap_inline52 2 tex2html_wrap_inline52 3 and 36 can be factored as follows: 36 = 4 tex2html_wrap_inline52 9 = 2 tex2html_wrap_inline52 2 tex2html_wrap_inline52 3 tex2html_wrap_inline52 3.
Rewrite both fractions where the denominators are in factored form.

tex2html_wrap_inline68 .

Multiply each fraction by the form of 1 that will yield denominators with the same set of factors. (i.e., you can find each set of factors in the denominator of the answer)

tex2html_wrap_inline27

Combine the numerator: 15 - 14 = 1. The answer is tex2html_wrap_inline74 .
This answer is already reduced.

Check:
Now prove to yourself with your calculator that your answer is correct. Calculate 5 divided by 24, 7 divided by 36, and combine the answers.. Now divide 1 by 72. Both answers should be the same. If you are correct, the answers are the same (equivalent) and you have successfully added two fractions.

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Author:Nancy Marcus

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