Visualize Fractions: example 4.17

Draw a number line. Mark $0$ in the middle and then mark several units to the left and right.

To locate $\frac{1}{4},$ divide the interval between $0$ and $1$ into four equal parts. Each part represents one-quarter of the distance. So plot $\frac{1}{4}$ at the first mark.

To locate $-\frac{1}{4},$ divide the interval between $0$ and $\mathrm{-1}$ into four equal parts. Plot $-\frac{1}{4}$ at the first mark to the left of $0.$

Since $1\frac{1}{3}$ is between $1$ and $2,$ divide the interval between $1$ and $2$ into three equal parts. Plot $1\frac{1}{3}$ at the first mark to the right of $1.$ Then since $\mathrm{-1}\frac{1}{3}$ is the opposite of $1\frac{1}{3}$ it is between $\mathrm{-1}$ and $\mathrm{-2}.$ Divide the interval between $\mathrm{-1}$ and $\mathrm{-2}$ into three equal parts. Plot $\mathrm{-1}\frac{1}{3}$ at the first mark to the left of $\mathrm{-1}.$

To locate $\frac{5}{2}$ and $-\frac{5}{2},$ it may be helpful to rewrite them as the mixed numbers $2\frac{1}{2}$ and $\mathrm{-2}\frac{1}{2}.$

Since $2\frac{1}{2}$ is between $2$ and $3,$ divide the interval between $2$ and $3$ into two equal parts. Plot $\frac{5}{2}$ at the mark. Then since $\mathrm{-2}\frac{1}{2}$ is between $\mathrm{-2}$ and $\mathrm{-3},$ divide the interval between $\mathrm{-2}$ and $\mathrm{-3}$ into two equal parts. Plot $-\frac{5}{2}$ at the mark.