Adding Fractions with different denominators (Finding equivalents).

When adding fractions with different denominators the aim is to make the denominators the same and then to proceed as before, with fraction with the same denominators. e.g.

This is exactly the same calculation we did in the last section but in the simplified form. Children need to understand that that one half is equivalent to two quarter.

e.g.

By using this as an example your child can see the reasoning behind equivalent fraction, i.e. to go from a half to a fraction we begin take our whole, already cut into halves, and we must cut it into quarter. Therefore to convert the denominator from 2 to 4 ( x 2) we must also convert the numerator from 1 to 2 ( x 2 ) to maintain the value). Essentially, what we do to the denominator we must do to the numerator to maintain the value.

e.g.

Here we have to find the equivalent to one sixth in thirds, to be able to add these fractions.

e.g.

We can see that to get from 3 to 6 we had to multiply by 2, thus we must do the same to the numerator and multiply 1 by 2.

e.g.

Diagrammatically we can see that by converting the shape from 3 parts to 6 parts, and the denominator from 3 to 6, the number of blue parts (representing the numerator ) also doubles.

Once both our fractions are sixths we can easily add them.

The process is exactly the same when dealing with non-unitary fractions.

e.g.

As before, we need both fractions to have the same denominator. The first fraction (two thirds) must be converted to sixths i.e. the denominator, 3, is once again multiplied by 2 to get a denominator of 6 (sixths).

As the diagram shows, if the denominator (number of parts in the whole) is doubled, the numerator must also be doubled (number o blue parts). The fact that the numerator is 2 this time, just means we multiple 2 by 2.

e.g.

We can then easily add one sixth to four sixths.

The last step of any addition will be to ensure our answer is presented in it simplest form, I will cover that in another bog.