Simplifying Fractions

This week, I am focusing on simplifying fractions. This is an important step whenever you are working with fractions, and is used for multiple operations. Simplifying fractions is pretty straightforward, but can be difficult to explain to elementary students. Therefore, having a clear and concise way to share this with elementary students is important.

While researching online, I came across several great resources. I found this particular resource from MathIsFun to be very straightforward, visual and helpful. It explains that the definition of simplifying fractions is to reduce the fraction -- or make it as simple as possible. For example, 4/8 can be simplified to 1/2. Using a pizza pie is a great way to illustrate this to young students, which is exactly what MathIsFun did. In the below example, they take a pizza pie and split it up into 8 sections, then highlight four of those sections to illustrate 4/8. Next, they show that 4/8 is equivalent to 2/4, by taking the same pizza pie and now splitting it up into 4 pieces, then highlighting 2 slices. Lastly, they show that 2/4 is equivalent to 1/2, by taking the same pizza pie, splitting it into 2 pieces, and then highlighting one piece.

This illustration is a great example to use when explaining this concept to elementary students because it is extremely visual. Students can see that visually, 4/8, 2/4 and 1/2 all look the same. By using an illustration such as the one above, students will also understand that even though the fractions look different, they take up the same amount of space on the pizza pie, and therefore are equal.

The next method that MathIsFun uses is the "greatest common factor" method, which is typically what I use when simplifying fractions. For this method, the student should think about the greatest factor that goes into both the numerator and denominator. So, let's take the example above. If we have 4/8, a common factor that goes into both numbers is 2. 4/2=2, and 8/2=4, making your new fraction 2/4. But...is that the GREATEST common factor? NO! Yes, it is one factor that goes into both numbers, but then you're left having to simplify again, because 2/4 can be simplified further by dividing by 2 again, resulting in a simplified fraction of 1/2.

So let's try simplifying the same fraction again by the GREATEST common factor this time. 4 goes into both 4 and 8, and there is no great number that goes into both of these numbers, meaning 4 is the GREATEST common factor. 4/4=1, and 8/4=2, making your new fraction 1/2, just like the pizza pie above.

See below for another example:

Next week, I will begin focusing on mixed fractions. These are slightly more complicated to work with, but elementary students are expected to add, subtract, multiply and divide mixed fractions as part of the core curriculum as well. Tune in next week!