4.1 Visualize fractions  (Page 6/11)

Solution

Start by locating the proper fraction $\frac{3}{4}.$ It is between $0$ and $1.$ To do this, divide the distance between $0$ and $1$ into four equal parts. Then plot $\frac{3}{4}.$

Next, locate the mixed number $4\frac{1}{5}.$ It is between $4$ and $5$ on the number line. Divide the number line between $4$ and $5$ into five equal parts, and then plot $4\frac{1}{5}$ one-fifth of the way between $4$ and $5$ .

Now locate the improper fractions $\frac{4}{3}$ and $\frac{5}{3}$ .

It is easier to plot them if we convert them to mixed numbers first.

Divide the distance between $1$ and $2$ into thirds.

Next let us plot $\frac{7}{2}.$ We write it as a mixed number, $\frac{7}{2}=3\frac{1}{2}$ . Plot it between $3$ and $4.$

The number line shows all the numbers located on the number line.

Solution

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.