Simplifying Fractions Graphically
I teach remedial math for the Army (adult learners). Since most people are visual learners, and fractions are where many of them have difficulty, I do a lot of drawing. I encourage students to draw as it helps them understand what’s going on physically. (Many tell me that they see fractions as just numbers flying everywhere. They really don’t have a grip on what the various numbers mean.) I was drawing out fractions, so the students could get a feel for what each fraction looked like, and came across something: it’s possible to do a lot of simplification, and some math, graphically. This process may also help grade schoolers struggling with the concept of fractions.
(Side Note: I use circles as fractions instead of rectangles as it’s just as important to see what’s missing, as what’s there. A rectangles with 2 lines through it could be 3, 3/4, 3/5, etc… These are all distinct with circles.)
By looking at the fractions, we can see when there’s a whole that can be removed from the calculation if we combine fractions or break fractions into pieces. For example, when we add 3/4 + 5/8 + 1/2 + 1/4, we can see that the 1/4 piece fits into the 3/4 piece. Those combine to a whole and eliminate 2 of the fractions.
