Adding and Subtracting Fractions

While multiplying and subtracting fractions is quite easy, add and subtracting is a bit more tricky.

You can only add halves to halves or quarters to quarters or tenths to tenths and so on. So if the fractions that you want to add don’t have the same denominator (number at the bottom) then they have to be changed so that they do.

The same number can be written in many different ways,

Here has been written in 6 different ways, but always the number at the top is half of the number at the bottom.

So if I want I can look along the list to find that , so that the same question becomes

Once both numbers are in quarters, they can be added, two quarters plus one quarter is three quarters.

Well that’s O.K., but is it necessary to write out a list of fractions to find some that have the same denominators? No, there another way.

A ‘common denominator’ is needed, a number which both 4 and 10 will divide into.

20 is the lowest common denominator, so we will use that.

To get the top numbers (the numerators), divide the common denominator by the denominator of the original question, then multiply by the numerator of the question,

20÷4x1 = 5

and 20÷10x3=6

and now the fractions can be added

Subtraction works in exactly the same way, except, of course, that you subtract at the end, instead of adding.

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Answers         Multiply and Divide Fractions