Question

Look at the figures and write $‘<’$or $‘>’,$ $‘=’$ between the given pairs of fractions.

$\left(a\right)\frac{1}{6}\boxed{}\frac{1}{3}$

$\left(b\right)\frac{3}{4}\boxed{}\frac{2}{6}$

$\left(c\right)\frac{2}{3}\boxed{}\frac{2}{4}$

$\left(d\right)\frac{6}{6}\boxed{}\frac{3}{3}$

$\left(e\right)\frac{5}{6}\boxed{}\frac{5}{5}$

Answer 1

Find the required symbol.

$\left(a\right)\frac{1}{6}\boxed{}\frac{1}{3}$

In the given expression, the numerator is the same.

So, the fraction with a small denominator will be large.

Hence, $\frac{1}{6}\boxed{<}\frac{1}{3}$.

$\left(b\right)\frac{3}{4}\boxed{}\frac{2}{6}$

Let us multiply the first fraction by $3$

$$\begin{gathered} \frac{3}{4}=\frac{(3\times 3)}{(4\times 3)} \\ \frac{3}{4}=\frac{9}{12} \end{gathered}$$

Let us multiply the second fraction by 2

$$\begin{gathered} \frac{2}{6}=\frac{(2\times 2)}{(6\times 2)} \\ \frac{2}{6}=\frac{4}{12} \end{gathered}$$

Since both fractions have the same denominators. Therefore, the fraction having a large numerator will be a greater number.

Hence, $\frac{3}{4}\boxed{>}\frac{2}{6}$.

$\left(c\right)\frac{2}{3}\boxed{}\frac{2}{4}$

In the given expression, the numerators are the same. Therefore, the fraction having a small denominator will be greater.

Hence, $\frac{2}{3}\boxed{>}\frac{2}{4}$.

$\left(d\right)\frac{6}{6}\boxed{}\frac{3}{3}$

On simplifying we get $\frac{6}{6}=1$ and $\frac{3}{3}=1$.

Hence, $\frac{6}{6}=\frac{3}{3}$.

$\left(e\right)\frac{5}{6}\boxed{}\frac{5}{5}$

In the given expression, the numerators are the same. So, the fraction having a larger denominator is lesser.

Hence, $\frac{5}{6}\boxed{<}\frac{5}{5}$.

Hence the required answers are

$\left(a\right)\frac{1}{6}\boxed{<}\frac{1}{3}$

$\left(b\right)\frac{3}{4}\boxed{>}\frac{2}{6}$

$\left(c\right)\frac{2}{3}\boxed{>}\frac{2}{4}$

$\left(d\right)\frac{6}{6}\boxed{=}\frac{3}{3}$

$\left(e\right)\frac{5}{6}\boxed{<}\frac{5}{5}$.