Adding fractions step by step

Adding fractions is a relatively common mathematical operation. Yet many people find it difficult, even though you only need to remember a few simple rules.

These things you need to know before adding fractions

Since everything in mathematics is built on each other, you can't add fractions without knowing the parts of the fractures and the the expansion of fractures.

Once you know this, it should be easy to add fractions from now on.

Addition of fractions with the same denominator

The easiest thing to do is to add fractions with the same denominator.

Fractions with the same denominator are added by adding their numerators and leaving their denominators unchanged.

Let's look at an example:

There is nothing else to do but add up the counters and do nothing with the denominator!

That's pretty simple, right?

However, the addition of fractions ends when the final result is simplified - provided that you can.

Addition of fractions with different denominators

The addition of fractions with different denominators is done in the same way, the only difference is that first common ground we have to bring them.

Fractions with different denominators are added by first bringing them to a common denominator, then adding the numerators, leaving the common denominator unchanged.

Let's look at an example of this!

First, we bring fractions into common ground:

Then add the numerators as before, leaving the denominators unchanged:

If you can't simplify, the addition of fractions is already done.

Addition of a fraction and a whole number

Adding a fraction and a whole number should not be a problem if you already know the steps above. The difference is that you have to convert the whole number into a fraction.

A fraction and an integer are added by rewriting the integer as a fraction so that its denominator is the same as the denominator of the fraction.

The numerators are then added and the denominator is left unchanged.

Let's look at this also through an example:

In this case you need to convert the 2 integers into quarters:

Then all you have to do is add the two numbers as above:

Finally, simplify if you can! This is not possible here, so we have already prepared the task.