math
6th Grade - Fractions

Grade 6 lesson

3 - Fractions


Comparaison and simplification of fractions

First of all, take note of something :
simplification of a fraction

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
fraction and fraction, as fraction comparison and that fraction comparison, 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:

simplifying a fraction

Adding fractions

We want to calculate adding fractions.
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 fraction et fraction, 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 : egalité de fractions and equality of fractions. 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 :
adding fractions


Another example : sum of fractions

Generally, if a, b, c, d are numbers and we want to calculate adding fractions, we must multiply fraction by d and fraction by b.
adding fractions, writing under the same denominator
adding fractions, writing under the same denominator

Subtracting fractions

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



See also : fractions on fmaths.com



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6th Grade Fractions

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