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!
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:
Formula: Adding Fractions NOT having Common Denominators
Two fractions that don't have the same denominators or common denominators cannot be added directly! Instead:
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.