Addition II - Fraction plus Fraction

Pizza Roma with lots of cheese, please!

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

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

Example: 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:

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