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### Addition of fractions

For several reasons, people find **addition of fractions** difficult. It's all very logical.

##### Example 1

On primary school you learned to calculate with fractions, such as

##### Example 2

Some fractions require more work

You must first make the denominators equal

A picture shows this clearly

• • • + • • • = • • • • • • • • • • • •

##### Example 3

Sometimes a fraction is quite tricky, but it always works in the same way

Two things are disturbing: the points and the minus sign. So we first find a solution for the commas

Well, those points are gone. Now make the denominators equal

and you see, the problem with the minus sign has resolved itself.

##### Example 4

We now make it even more difficult

Here the minus signs disturb even more than the point, so we handle them first

and for the rest we get

We can simplify this, and that works in a similar way

as you may divide the whole numerator and whole denominator by the same number.

##### Example 5

Now we are going to give it a try with letters, and you'll see that works just the same

You must first make the denominators equal

You will understand that *a × b* is the same as *b × a*, because 2 × 3 is, just as much as 3 × 2. In alphabetical order you write the answer as

##### Example 6

Nothing hinders us now to calculate the following fraction

Step by step we tackle this

We guess that the denominator should be 50*a*

The whole numerator and whole denominator can be divided by 10