Draw the number line and represent the following rational numbers on it:
$(i)$. $\frac{3}{4}$
$(ii)$. $\frac{-5}{8}$
$(iii)$. $\frac{-7}{4}$
$(iv)$. $\frac{7}{8}$

Given: Rational numbers:

$(i)$. $\frac{3}{4}$

To do: To draw the number line and represent the given rational numbers on it.

Solution: Here given rational numbers are represented on the number lines as below:

$(i)$. Representation of $\frac{3}{4}$ on the number line:

Let us draw a number line. As we know that $\frac{3}{4}$ is less than $1$. So, it will lie between $0$ and $1$. 

Let us divide the number line into four equal parts from $0$ to $1$.

Let us denote $\frac{0}{4},\ \frac{1}{4},\ \frac{2}{4}$ and $\frac{3}{4}$ on the number line. Here $\frac{0}{4}$ represents $0$ and $\frac{4}{4}$ represent $1$.

Mark $\frac{3}{4}$ on the number line.

$(ii)$. Representation of $\frac{-5}{8}$ on the number line:

Let us draw a number line. As we know that $-\frac{5}{8}$ is greater than $-1$. So, it will lie between $0$ and $-1$. 

Let us divide the number line into eight equal parts from $0$ to $-1$.

Let us denote $\frac{0}{8},\ -\frac{1}{8},\ -\frac{2}{8},\ -\frac{3}{8},\ -\frac{4}{8},\ -\frac{5}{8},\ -\frac{6}{8},\ -\frac{7}{8}$ and $-\frac{8}{8}$ on the number line. Here $\frac{0}{8}$ represents $0$ and $-\frac{8}{8}$ represent $-1$.

Mark $-\frac{5}{8}$ on the number line.

$(iii)$. Representation of $\frac{-7}{4}$ on the number line:

Let us draw a number line. As we know that $-\frac{7}{4}$ is less than $-1$ and it is greater than $-2$. So, it will lie between $-1$ and $-2$. 

Let us divide the number line into eight equal parts from $0$ to $-2$.

Let us denote $\frac{0}{4},\ -\frac{1}{4},\ -\frac{2}{4},\ -\frac{3}{4},\ -\frac{4}{4},\ -\frac{5}{4},\ -\frac{6}{4},\ -\frac{7}{4}$ and $-\frac{8}{4}$ on the number line. Here $\frac{0}{4}$ represents $0$ and $-\frac{8}{4}$ represent $-2$.

Mark $-\frac{7}{4}$ on the number line.

$(iv)$. Representation of $\frac{7}{8}$ on the number line:

Let us draw a number line. As we know that $\frac{7}{8}$ is less than $1$. So, it will lie between $0$ and $1$. 

Let us divide the number line into eight equal parts from $0$ to $1$.

Let us denote $\frac{0}{8},\ \frac{1}{8},\ \frac{2}{8},\ \frac{3}{8},\ \frac{4}{8},\ \frac{5}{8},\ \frac{6}{8},\ \frac{7}{8}$ and $\frac{8}{8}$ on the number line. Here $\frac{0}{8}$ represents $0$ and $\frac{8}{8}$ represent $1$.

Mark $\frac{7}{8}$ on the number line.

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Updated on: 10-Oct-2022

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