Question

Draw number lines and locate the points on them: (a) $\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$ (b) $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$ (c) $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Answer 1

(a)

Step 1. Draw a line and locate the points $\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$.

First, make the same denominator in all the fractions.

$\begin{array}{rcl}\frac{1}{2}& =& \frac{1}{2}\times \frac{2}{2}\\ & =& \frac{2}{4}\end{array}$

Now, the points are $\frac{2}{4},\frac{1}{4},\frac{3}{4},\frac{4}{4}$.

Draw a number line, mark two points $0$ and $1$ on it:

Divide the gap between $0$ and $1$ into four equal parts because denominator is $4$:

Now, first part will show $\frac{1}{4}$, second part show $\frac{2}{4}=\frac{1}{2},$ third part show $\frac{3}{4}$ and last part show $\frac{4}{4}$.

Hence, $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ represent $\frac{1}{4},\frac{1}{2},\frac{3}{4}$ and $\frac{4}{4}$ respectively.

(b)

Step 2. Draw a line and locate the points $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$.

Draw a number line, mark two points $0$ and $1$ on it:

Divide the gap between $0$ and $1$ into eight equal parts because denominator is $8$:

Now, first part will show $\frac{1}{8}$. Also, second part show $\frac{2}{8},$ third part show $\frac{3}{8}$, fourth part show $\frac{4}{8}$, fifth part show $\frac{5}{8}$, sixth part show $\frac{6}{8}$, seventh part show $\frac{7}{8}$ and last part show $\frac{8}{8}$.

Hence, $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ represent $\frac{1}{8},\frac{2}{8},\frac{3}{8}$ and $\frac{7}{8}$ respectively.

(c)

Step 3. Draw a line and locate the points $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$..

Draw a number line, mark two points $0$ and $2$ on it:

Divide the gap between $0$ and $1$ and between $1$ and $2$ into five equal parts because denominator is $5$:

Now, first part will show $\frac{1}{5}$. Also, second part show $\frac{2}{5},$ third part show $\frac{3}{5}$, fourth part show $\frac{4}{5}$, fifth part show $\frac{5}{5}=1$, sixth part show $\frac{6}{5}$, seventh part show $\frac{7}{5}$, eighth part show $\frac{8}{5}$, nineth part show $\frac{9}{5}$, and last part show $\frac{10}{5}$.

Hence, $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ represent $\frac{2}{5},\frac{3}{5},\frac{4}{5}$ and $\frac{8}{5}$ respectively.