Why Are So Many Students Bad At Fractions?

Why are so many Algebra 1 students bad at fractions? This is a question that has bothered me for a really long time. In fact, I have seen rates of over 90% when it comes to the number of students I’ve worked with who don’t understand how to do basic operations on fractions. While one of the obvious answers to this question is that fractions seem scary, I think this is a really bad reason because the basic operations on fractions can be taught in less than an hour if you use the correct order. Here’s an example of what I mean.

First, students should learn multiplication with fractions. This is easy since you just multiply straight across, like so:

\frac{2}{5} * \frac{3}{7} = \frac{2*3}{5*7} = \frac{6}{35}

This takes all of 3-5 minutes to teach. Now we add in division by teaching students to change it into multiplication by flipping the second fraction. Then you get something like this:

\frac{3}{4} \div \frac{2}{3} = \frac{3}{4} * \frac{3}{2} = \frac{3*3}{4*2} = \frac{9}{8}

Assuming this takes another 5 minutes, we’re now 10 minutes into the lesson and have covered both multiplication and division. Next, I suggest that you show students how to change the denominator of a fraction. For example, if we want to change the denominator of to 9, then we do the following multiplication:

\frac{2}{3} * \frac{3}{3} = \frac{2*3}{3*3} = \frac{6}{9}
\frac{3}{3} = 1

Notice that the students should understand that, but they’ll already know how to do the multiplication. Next, you should show students that sometimes you’ll want two fractions to have the same denominator, and show them the concept of a common denominator.

With that out of the way, it’s time for addition and subtraction. We show that first we need the same denominator, and then just add or subtract the numerators. For example:

\frac{3}{7} + \frac{2}{7} = \frac{3+2}{7} = \frac{5}{7}

Since students already know how to find a common denominator, all that’s needed is to work through examples with the students from this point since all of the necessary theory has already been covered.