Adding Fractions

Welcome to Adding Fractions!

This is a tutorial on how to add fractions.

What Are Fractions?

First let's discuss what fractions are.

Let's say you were throwing a pizza party. How many pizzas would you like to serve? 1 pizza? 2 pizzas? 3 pizzas?

If it's a small pizza party (with perhaps just you and a friend), 1 pizza might already be too much food. Maybe you want to order less than one whole pizza.

Fractions allow you to describe numbers that are less than 1. For example, if you divide a whole pizza into three equal pieces and eat one of those pieces, then you ate 1/3 ("one third") of the pizza.

Adding Fractions comes with a calculator to help you understand fractions. Go to the calculator page, and try entering the fraction 1/3 into the calculator's text box. If you press the calculator's "Try It" button, you will then see a picture representing 1/3. Note that in the picture, the circle is divided into 3 equal pieces, one of which is shaded in blue. The blue piece represents the fraction 1/3.

How To Add Fractions

Suppose you ate 1/3 of the pizza, and your friend ate 1/4 of the pizza. How much pizza did you two eat combined?

To answer this question, we need to add the amounts that you two ate: We need to calculate 1/3 + 1/4.

Try entering the expression 1/3 + 1/4 into the calculator. The calculator will return a step-by-step explanation of how to add 1/3 and 1/4, to get 7/12.

Let's walk through the calculator's explanation to see how to add these fractions. Recall that you ate 1/3 of the pizza, and your friend ate 1/4. In the calculator's explanation, note that 1/3 is shown in blue, and 1/4 is shown in green.

Since the blue piece and the green piece are different sizes, it's not obvious how to add them.

However, what if we cut each pizza into 12 equal slices?

You ate 1/3 of the pizza, which is equal to 4 of the 12 slices. Your friend ate 1/4 of the pizza, which is equal to 3 of the 12 slices. Together, the two of you ate 7 slices out of 12, which is equal to the fraction 7/12.

Hopefully this explanation made some sense.

If you would like to try different examples of adding fractions, there are more examples to try on the Examples page.

Other Resources

Here are some other suggestions of tutorials on adding fractions: