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How To Add And Subtract Mixed Fractions

By Edited Oct 15, 2016 0 0

Performing algebraic operations with mixed fractions works just same as with typical fractions. The only difference is that when working with mixed fractions, one must convert them into the form of a standard fraction or in this case an improper fraction. This article will show you how to convert mixed fractions into improper fractions so that they can be added and subtracted.

The mixed fraction consists of three parts: a whole number, numerator and a denominator. A mixed fraction is simply the representation of a fraction with a numerator that is greater than its denominator. In mixed fraction form the denominator is divided into the numerator resulting in a whole number term along with a remainder left as a numerator divided by the original denominator. For example, if we have the improper fraction of 12/5, we convert this into a mixed fraction by dividing the denominator 5 into 12 leaving the remainder of numerator 2 divided by the denominator of 5. So we this will give us12/5 = 2 2/5.

Now before adding or subtracting fractions that are in the mixed form, we must convert them into the improper fraction form. To do this we must simply work backwards from the procedure outlined above. With a mixed fraction, you must recognize that the whole number integer represents the number of times the denominator could be divided in to the improper fraction numerator. So to convert the mixed fraction into the improper fraction form, we must multiply the integer whole number by the denominator and add the remainder (the numerator of the mixed fraction) to get the numerator of the improper fraction. As an example, we have the mixed fraction of 3 3/7 and want to convert it into an improper fraction. So we multiply 3 x 7 = 21 and add 3 and this gives us 24, this is the numerator for the improper fraction. So the improper fraction is 24/7. We can check this by converting it back to a mixed fraction to see if we are correct. Here we have

24/7 = 3 3/7, because 7 divides into 24, 3 whole times leaving a remainder of 3, resulting in our answer.

Let's look at a few examples.

1.) 12 5/14 + 5 3/8 = ((12 x 14) + 5)/14 + ((5 x 8) + 3)/8 = 173/14 + 43/8

So we need to rewrite these fractions into the form where the denominators are the same.

173/14 + 43/8 = (173 x 8)/(14 x 8) + (43 x 14)/(8 x 14) = 1384/112 + 602/112 = 1986/112

We will write the answer in to the form of a mixed fraction.

1986/112 = 17 82/112, we can further simply this mixed fraction to 17 41/56

2.) 5 2/3 – 4 1/8 = ((5 x 3) + 2)/3 – ((4 x 8) + 1)/8 = 17/3 – 33/8

17/3 – 33/8 = (17 x 8)/(3 x 8) – (33 x 3)/(8 x 3) = 136/24 – 99/24 = 37/24

We will rewrite this fraction into mixed fraction for leaving us 37/24 = 1 13/24.

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