Fractions

Introduction

A fraction has two parts numerator which as the top and denominator which is at the bottom.

You can not simply add the numerator and denominator of two fractions. For example, we know a half plus 2 quarter is one but using that logic 1/2+2/4=3/6. THIS IS WRONG!

A mixed number combines an integer and a fractional part. For example, 41/2 is a mixed number. When adding/subtracting fractions and mixed numbers the most important part is to find a common denominator. That is, the fractions should have the same denominator.

Examples:

Work out 1/2 + 2/4

Before we can add any fractions we must convert the fractions to a common denominator. This is found by finding the first common multiple of 2 and 4 which is 4.

Now we have to convert both fractions to the common denominator of 4 by multiplying the numerators and denominators of both fractions by 2 and 1 respectively: 2/2 x 1/2 = 2/4 and 1/1 x 2/4 = 2/4

Now the fractions have the same denominator we simply add the numerators together to get: 2/4 + 2/4 = 4/4 = 1

Work out 4 2/5  +  5 1/3

When adding mixed numbers you can make life easier for yourself by first adding the whole numbers together. In this case 4 + 5 = 9. Now we just have to work out the remaining fraction sum 2/5 + 1/3

The common denominator of 15. So we multiply the of both fraction by 3 and 5 respectively. 

3/3 x 2/5 + 5/5 x 1/3 = 6/15 + 5/15 = 11/15

Finally, remember to add on the 9 from the beginning of the questions to get: 

9 11/15