Question

Put $<\text{or}>$ sign in the box

$7\frac{1}{2}\times \frac{1}{6}\left(\right)6\frac{3}{4}\times \frac{2}{5}$

Answer 1

Step 1 : Find the product

LHS :

$$\begin{gathered} =7\frac{1}{2}\times \frac{1}{6} \\ =\frac{15}{2}\times \frac{1}{6} \\ =\frac{5}{4} \end{gathered}$$

RHS :

$$\begin{gathered} =6\frac{3}{4}\times \frac{2}{5} \\ =\frac{27}{4}\times \frac{2}{5} \\ =\frac{27}{10} \end{gathered}$$

Step 2 : Find the greatest fraction.

Take LCM of $\left(4,5\right)=20$

Now, convert the fractions into equivalent fractions.

$$\begin{gathered} \frac{5}{4}=\frac{5\times 5}{4\times 5}=\frac{25}{20} \\ \frac{27}{10}=\frac{27\times 2}{10\times 2}=\frac{54}{20} \\ \because 25<54 \end{gathered}$$

So,$\frac{5}{4}<\frac{27}{10}$ [In equivalent fractions, fractions with smaller numerators are smaller]

$\text{Hence,}7\frac{1}{2}\times \frac{1}{6}<6\frac{3}{4}\times \frac{2}{5}$