Adding fractions for grades 2 to 4

Add fractions with the same denominators

Adding two fractions where the denominators of the fractions (the numbers below the lines) are the same is quite straightforward. Your answer will have the same denominator as the fractions you are adding, and the numerator (the number above the line) will be the sum of the numerators of the fractions you are adding. For instance, adding one fifth and two fifths:

You can see in the example above that both fractions have a denominator of 5. So the answer will have a denominator of 5. Adding the numerators gives us 1 + 2 which is 3, so the answer is three fifths which makes sense intiuitively if you think what the answer "should" be. You have one fifth of a cake and your friend has two fifths of a cake so together you have three fifths of the cake.

What if the answer is a "top-heavy" fraction?

What happens if we have the same denominators in the question but in the answer the numerator is greater than the denominator (e.g. seven over six)? Then your answer is what is called a "top-heavy" fraction (heavier on the top than the bottom..). It is fine for your answer to stay like that, as a top-heavy fraction, but sometimes you are asked to convert top heavy answers to so called "mixed fractions".

A mixed fraction is a combination of an integer and a fraction like one and a half or two and a quarter. Converting from a top-heavy to a mixed fraction involves dividing the numerator by the denominator, keeping the whole answer as the integer, and the remainder as the numerator of the fraction part of the mixed fraction. For instance, the top-heavy fraction three over two converts to the mixed fraction one and a half.

Add fractions with different denominators

Things get a little more involved when the denominators of the two fractions you have been asked to add are not the same. Say we are asked to add one half and one quarter. What we need to do is change one or both of those fractions so that the denominators are the same. The way we do this is by multiplication.

If you remember that a fraction can be thought of as a ratio between numerator and denominator, you can see that if we multiply both numerator and denominator by the same number, the fraction retains it's ratio even though the values of numerator and denominator have changed.

When adding a half and a quarter, we can see that we need to multiply the numerator and denominator of a half by two.

This converts a half into the equivalent fraction two over four. Now both of our fractions have the same denominator, so we can add them as we learned earlier.

In the example above, we only had to change one of the fractions to be able to add them. Sometimes we need to change both fractions to get the same denominators. For instance, if we add two fifths and one third, you can see that we will need to multiply both fractions to get the denominators the same. In fact we will need to multiply each fraction by the denominator of the other fraction.

The takeaway idea from this is: if the denominators are the same, simply add the numberators and you are done. If the denominators are different, use multilication to change one or both of the fractions so that their denominators are the same before adding them. You can practice what you have learned here at Free Math Games. Go to Start → select your grade, year or age → select Fractions → select Addition.