Fractions: Adding fractions

All right, now that we have the easy skills out of the way, we’re going to tackle one of the harder fraction skills. Amazingly, adding fractions is very confusing for many people, and it really doesn’t need to be.

To really understand what we’re doing, I need you to think of the denominator as a unit instead of a number. You know how you combine inches with other inches and still get inches. Adding fractions if the same idea. You add fifths and still get fifths. It will help if you get into the habit of calling a fraction by its proper name.

Let’s try this. We’re going to add one fifth to two fifths. Note that we’re calling them by their actual names. The problem looks like this mathematically:

+

Your first instinct might be to add the two together and come up with , but remember what I said earlier. Those fifths aren’t numbers. They’re units we’re putting together. We know we have one of them in one group, and two of them in the other group, so we’re still going to have fifths at the end of the problem.

+ =

We added one fifth to our two fifths, and found out we have three fifths all together.

But what happens if we’re trying to add one fifth to three tenths. Suddenly, we don’t have the same units! When we see problems like this that involve feet and inches, we just convert the feet to inches and add all of the inches together. It’s the same thing with fractions. We change the fractions until the have the same unit (you can change just one fraction or both fractions, depending on the problem).

In our case, we have fifths and tenths. Well, we know the five is a factor of ten, so we can change that one fifth into tenths. Five goes into ten twice, so we’re going to create an equivalent fraction of two tenths. We now have two tenths and three tenths to add together. The problem goes fairly simply at this point.

+ =

When we add those two tenths to our three tenths, we end up with five tenths. (If you want, you can practice simplifying that answer.)