Finding Common Denominators of Rational Expressions Activity

Do your students struggle finding common denominators when adding and subtracting rational expressions? I created this finding common denominators activity a few years ago when I was teaching Algebra 2.

I found that my students needed plenty of practice identifying what the least common denominator should be before we ever spent time practicing how to rewrite the rational expressions with common denominators.

My students completed this finding common denominators activity in groups. Each group received a bag of laminated cards.

After each group received their bag of cards, I had them lay out all of their cards on their desks so all of the group members could see their bank of choices.

I printed the cards on two different colors of paper. I printed the exponents on a different color of paper to make it clear that those cards were exponents.

Note: the group above has two 6 cards. One of those should have been flipped over to form a 9. Even if students make this mistake, they should be able to figure it out if they end up needing a 9.

The actual structure of the activity is quite simple.

1. Display a problem involving adding or subtracting rational expressions for students to see. You can do this via technology and a SMARTBoard/Projector/other interactive touchscreen device or you can go old-school and write the problem on your dry erase board or chalk board.
2. Students work in groups to determine the least common denominator of the expressions.
3. Each group must use their colored cards to “build” the common denominator.
4. After each group has submitted a solution, compare answers. Discuss common mistakes or the common case of students identifying a common denominator that will work but is not the LEAST common denominator. I always remind students that this is okay, but it can sometimes lead to a lot of extra work for students.

When I originally did this activity with my students back in 2019, I just had a list of handwritten expressions on a notepad. To make it easier for other teachers to use this activity with their students, I decided to type up a list of rational expressions that this deck of cards will work for.

The goal is not for students to actually perform the given operation but to only determine what the least common denominator will be.

For your convenience, I have also included an answer key featuring the common denominators.

The activity is specifically designed to encourage students to FACTOR the expressions before trying to find a common denominator.

You could also print and use the list of questions as a worksheet if you so desired. In fact, you could probably assign it as a worksheet after completing this activity without students even realizing they are the same problems!