SUBTRACTION: Problem 3

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.

Problem 3:

Calculate

and reduce your answer.

Answer:

The answer is

Solution:

The denominators are different, so you must build each fraction to a form where they both have the same denominator. Rewrite the problem with the denominators factored.

tex2html_wrap_inline74 . The common denominator must contain the factors 2, 5, and 7.

Build each fraction using the number 1, so that both denominators will have these three factors.

tex2html_wrap_inline76 and tex2html_wrap_inline78 .

tex2html_wrap_inline70 can now be written tex2html_wrap_inline82 .

Combine the numerators: 49 - 15 = 34.
The answer is tex2html_wrap_inline86 .

The answer can be reduced further to tex2html_wrap_inline88 .

In grade school you probably ran a slashed line on the two's without realizing what gave you the right to do it. As long as you realize what gives you the right to do it, you can use that shortcut in these problems.

Check:

Now prove to yourself with your calculator that your answer is correct. Calculate 7 divided by 10, calculate 3 divided by 14, and combine the results. Now divide 17 by 35. Both answers should be the same. If you are correct, the answers are the same (equivalent) and you have successfully combine two fractions using subtraction.

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