The model for the fraction \(\displaystyle\frac{{3}}{{4}}\) is shown below. You can thing a circular pizza. Now divide it 4 equal slices. Then \(\displaystyle\frac{{3}}{{4}}\) represent three pizza slice.

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

The model for the fraction \(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\). First note that

\(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}={2}\cdot{5}+\frac{{3}}{{5}}=\frac{{13}}{{5}}\)

You can think you have three circular pizzas. Now divide it each pizza by 5 equal slices. Then you have total \(\displaystyle{5}{x}{3}={15}\) slices. Then \(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\) represent total 13 pizza slices. That meants two complete pizza and three slices from the third pizza.

\(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\)

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

The model for the fraction \(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\). First note that

\(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}={2}\cdot{5}+\frac{{3}}{{5}}=\frac{{13}}{{5}}\)

You can think you have three circular pizzas. Now divide it each pizza by 5 equal slices. Then you have total \(\displaystyle{5}{x}{3}={15}\) slices. Then \(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\) represent total 13 pizza slices. That meants two complete pizza and three slices from the third pizza.

\(\displaystyle{2}{\left(\frac{{3}}{{5}}\right)}\)