6th Grade - Fractions

# 3 - Fractions

## Comparaison and simplification of fractions

First of all, take note of something :

If we multiply the numerator and the denominator of a fraction by the same number, the value of the fraction does not change. This is a useful trick to compare fractions (say which one is larger than the other). For example, to compare
and , as and that , it is which is the smaller of the two. Conversely we have the right to divide the numerator and the denominator of a fraction by the same number. This enables us to simplify a fraction by writing it with smaller numbers:

We want to calculate .
In order to add two fractions and obtain the result in the form of a fraction, we must use quite a special technique. In the same pattern that we cannot add potatoes and carrots (except to make some delicious soup but which still lacks some leeks), we cannot add thirds and fifths. To add et , the technique consists in transforming the two fractions so that they both have the same denominator. By multiplying the first fraction by 5 on top and at the bottom, and the second by 3 on top and at the bottom, we get : and . Now we have the right to add fifteenths and fifteenths, and as twenty over fifteen plus twenty-one over fifteen gives us forty-one over fifteen, we have :

Another example :

Generally, if a, b, c, d are numbers and we want to calculate , we must multiply by d and by b.

## Subtracting fractions

For subtraction, it is exactly the same thing, you must rewrite the two fractions over the same denominator then do the subtraction: