What Does it REALLY Mean to Simplify a Fraction?

Teaching fractions to students can sometimes become complicated especially when the teacher relies on how he or she was taught fractions. I can remember when I was in school my teacher would call simplifying a fraction reducing. When I realized that I loved math so much I decided to stop teaching  5th grade math and science and enter the world of  middle school math. By the time I began teaching middle school the words reducing fractions had been stricken from the list of math vocabulary words and replaced with simplifying fractions. At first I was confused as to why reducing fractions had been changed to simplifying fractions. So, I decided to dig a little deeper and look up the word simplify. The definition of simplify means to make less complex or complicated; make plainer or easier. I began to wonder how does this definition apply to teaching fractions.

I realized when working with fractions the denominator is always the focus. This also holds true when applying the word simplify to a fraction. In the picture the fraction 3/9 has 9 parts and is not in simplest form because there are 9 individual parts that are is apart of the fraction. In the world of fractions a fraction that has several parts is more complicated or complex.

To make a fraction less complicated or complex a student must be able to divide the nine parts into equal groups while keeping the numerator together in a group or multiple groups. Also each group must have the most color tiles that will fit into each group so that the fraction cannot be divided equally again. When the fraction 3/9 is grouped an equivalent fraction is created. The fraction 1/3 is in simplest form because the fraction began with 9 individual parts and now has 3 groups.

The Common Core Standards has made simplifying fractions a 4th grade math standard.  When teaching this standard I realized that my students must understand that a fraction can be decomposed into units that make up the whole fraction. After grasping the understanding of decomposing  they learned that a unit of a fraction could be divided to create an equivalent fraction, however it was understood that if they were going to divide one unit all of the units had to be divided because the units were all connected. While I was teaching this lesson one of my students realized that when you divide the units it is was like multiplying. I was so thrilled that she could make the connection between multiplication and dividing each unit because this made it very easy for me to teach the students how to create an equivalent fraction through multiplication.

When I taught my 6th grade students how to simplify fractions using color tiles in 2007 I had no idea that 5 years later that I would be teaching my 4th grade students the same concept. This experience has lead me to believe that if students understand the meaning of simplifying as it is applies to fractions then any student with the proper foundation in fractions can simplify fractions with ease. If you would like you try simplifying fractions using color tiles you can get your lesson plan today!