Introduction

Fraction Models

In this video, we will go over how to use models to represent fraction division.

\(\mathsf{ \frac{5}{4} }\)

Our first example is \(\mathsf{ \frac{5}{4} }\). We can write this fraction as 5 ÷ 4, which represents 5 wholes broken into 4 groups. Let’s model out 5 wholes and 4 groups. We can take 1 whole and put it in each group. We are left with 1 whole. Now we split this whole into 4 equal-sized parts. Each part is \(\mathsf{ \frac{1}{4} }\). We can put one of the parts in each group. Each group has \(\mathsf{ 1\frac{1}{4} }\). \(\mathsf{ \frac{5}{4} }\) or 5 ÷ 4 is \(\mathsf{ 1\frac{1}{4} }\).

\(\mathsf{ \frac{8}{6} }\)

\(\mathsf{ \frac{8}{6} }\) is 8 ÷ 6. We can make 8 wholes and 6 groups. We put 1 whole in each group. We are left with 2 wholes. We split each whole into 6 equal-sized pieces. Each piece is \(\mathsf{ \frac{1}{6} }\) of a whole. Now we split the pieces among the 6 groups. Each group has one whole and \(\mathsf{ \frac{2}{6} }\), so each group has \(\mathsf{ 1\frac{2}{6} }\). \(\mathsf{ \frac{8}{6} }\) or 8 ÷ 6 is \(\mathsf{ 1\frac{2}{6} }\).

\(\mathsf{ \frac{4}{3} }\)

\(\mathsf{ \frac{4}{3} }\) is 4 ÷ 3. We put 1 whole in each group and are left with 1 whole. We split the 1 whole into 3 equal-sized pieces. Each piece is \(\mathsf{ \frac{1}{3} }\). We put \(\mathsf{ \frac{1}{3} }\) in each group. Each group has \(\mathsf{ 1\frac{1}{3} }\). \(\mathsf{ \frac{4}{3} }\) or 4 ÷ 3 is equal to \(\mathsf{ 1\frac{1}{3} }\).