ADDITION: Example 4

Rule 18:
To add fractions, the denominators must be equal. Complete the following steps to add two fractions.
1.
Build each fraction so that both denominators are equal.
2.
Add the numerators of the fractions.
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 = 2 tex2html_wrap_inline52 12 and 36 can be factored as follows: 36 = 3 tex2html_wrap_inline52 12.
Rewrite both fractions where the denominators are in factored form.

tex2html_wrap_inline56 .

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

Add the numerators for the numerator in the answer.
15 + 14 = 29. The answer is tex2html_wrap_inline60 .
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 add the answers.. Now divide 29 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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