How do you help your students really understand the “why” behind the “how” when it comes to simplifying fractions? Here are a few strategies I find helpful:
Before we get into the pencil/paper strategies for solving the problems, it is always a good idea to start with something concrete: math counters, jellybeans, marbles, etc. Students can work to see if there are ways to make equal groups with the numbers in the numerator and denominator.
From the counters, students can progress into making dot pictures. This is a strategy students can then use with their paper and pencil practice later if they aren’t ready to go use the Greatest Common Factor or Prime Factors strategies.
Once students are ready to work with abstract, this is a good time to show them how to use the Greatest Common Factor of the numerator and denominator. You can show students how this connects to the counters and dots by showing them that when they are grouping the counters (or the dots) they are really dividing:
And now, for my two favorite paper/pencil methods for simplifying fractions:
The first is to use the Greatest Common Factor (GCF) This is also the way I remember learning back in the “olden days”. It still works today! First students list the factors of the numerator and the factors of the denominator. The GCF is the largest factor that they have in common. Divide the numerator and denominator by the GCF and viola, you have the simplest form!
The second is to use prime factors of the numerator and denominator and cross out any numbers that are the same because they equal one. For this one, you first make a prime factor tree for the numerator and one for the denominator. Then you rewrite the numerator and denominator as number sentences of their prime factors. Any numbers that are on both the top and bottom can be crossed out because they make one whole.
With some fractions you have to multiply the factors that are left like in the example below.