## Addition II - Fraction plus Fraction

I think we deserve a pizza!

I take the Pizza Roma with salami, ham and champinions - but with lots of cheese, please!

And You?

Because the pizzas are very big, there is still something left from both of us:

^{1}/_{3} of my Pizza Roma and

^{1}/_{4} of your pizza

Is it enough to feed anyone else? To answer this we have to add both fractions:

## Common mistake when adding fractions

A common mistake is, that - similar to the multiplication of fractions - both the numerators and the denominators are added:

Sadly, it's not that simple. Let's see if it makes sense:

The numerator indicates the number of pieces of pizza: 1 + 1 = 2.

The denominator indicates how big the pieces are. This means: the greater the denominator, the smaller the pieces of pizza. Therefore two pieces of the size of a "seventh-pizza" are of course smaller than one piece of the size "third-pizza" plus another one of the size "quarter-pizza".

With fractions you can only add up if the **denominators are the same size**.

## Formula: Adding Fractions having Common Denominators

*Two fractions having the same denominators or common denominators are added by adding the numerator. The denominator remains unchanged.*

The result often can be simplified / reduced:

^{1}/

_{8}+

^{3}/

_{8}

## Formula: Adding Fractions NOT having Common Denominators

*Two fractions that don't have the same denominators or common denominators cannot be added directly! Instead:*

- Make the denominators the same by expanding or simplifying / reducing (→ see simplifying / reducing).
- Add the numerators - the denominator remains unchanged.
- Check, if you can simplify the fraction (to lowest terms).

^{1}/

_{3}+

^{1}/

_{4}

Let's come back to the pizza:

In this case the denominators are not the same, so we cannot add the two fractions directly.

Have a look in our toolbox and pick the right one: Common Denominator - then we can use the formula to add fractions that have the same denominator:

In order to get a common denominator, expand the first fraction by 4 and expand the second fraction by 3. Afterwards, the numerators are added up:

## Online Practice: Adding Fractions

Here you can practice adding fractions online: Adding Fractions.

If you have any problems with the exercise, please have a look at the **hint** and the **sample solution** first.