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Math Basics: How To Subtract Fractions

By Edited Nov 13, 2013 0 1

A fraction by its very definition is a piece of data used to represent a fact. Fractions can be likened to percentages, ratios and decimals in that they all present a numeric piece of information considered as it relates to a whole data set. In this article you will find an explanation of how to subtract fractions with or without like denominators.

Each fraction includes a numerator and a denominator. The numerator is the top portion of a fraction and is the term that we are interested in as it relates to the whole data set, the denominator which is the bottom term of the fraction.

Much like when adding fractions, to subtract fractions the denominators of each must be common or the same. If you have two or more fractions with common denominators, the subtraction process is quite simple. The denominators represent the total amount and so we find the difference of the numerators with respect to that amount. For example, 13/18 – 5/18 = (13 – 5)/18 = 8/18 = 4/9.

If you are finding the difference of two or more fractions with unlike denominators, we have to perform a little bit of work. Since we know that the denominators must be common we have to utilize one of a couple of methods to accomplish this. One method involves the multiplying of a fraction (both the numerator and denominator) by some factor such that its denominator will become the same as that of the other fraction used in the subtraction calculation. Here's a quick example.

14/24 – 10/16 – 5/12 = ?

Let's write the second and third fractions such that they will have denominators equivalent to the denominator of the first fraction, 24. In a situation like this we could have chosen to write the fractions such that all the denominators are equal to 16 or 21 just the same.

We can recognize that the second fraction (both the numerator and denominator) can be multiplied by 3/2 to transform the denominator of 16 into 24. Likewise, we see that in the third fraction, the denominator is 1/2 of the first fraction, so to make it become 24 we multiply it by 2.

14/24 – (10 x 3/2)/(16 x 3/2) – (5 x 2)/(12 x 2) = ?

14/24 – 15/24 – 10/24 = ?

(14 – 15 –10)/24 = –11/24

We will now consider the case where we are working with multiple fractions that have different denominators that cannot be reduced or multiplied by an integer factor. Here we just have to recognize that the denominator of each fraction can be multiplied by the denominator of the other to create a new denominator that is appropriately factored for each fraction. Since we have multiplied a term by the denominator of each fraction, by the rules of algebra we must also multiply the numerator of each fraction by that same term. Let's see what this looks like in an example.

11/16 – 14/34 – 3/21 = ?

We will perform the previously outlined procedure in a stepwise manner. First, we will work with the first and second fractions, to create the first "difference fraction" and then work with this new fraction with the third fraction.

11/16 – 14/34 = ?

(11 x 34)/(16 x 34) – (14 x 16)/(34 x 16) = ?

374/544 – 224/544 = 150/544 = 75/272 (This is the "difference fraction")

We will now perform this process with the "difference fraction" and the third fraction.

75/272 – 3/21 = ?

(75 x 21)/(272 x 21) – (3 x 272)/(21 x 272) = ?

1575/5712 – 816/5712 = ?

(1575 – 816)/5712 = 759/5712 = 253/1904 (This is our final fraction)



Jan 20, 2011 9:56am
Never was good at fractions...I cheated with a fraction calculator. great advice...Thanks BA.
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