Question

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$\frac{1}{2}\times \frac{2}{3}\times \frac{3}{8}\left(\right)\frac{1}{7}\times \frac{2}{3}\times \frac{7}{8}$

Answer 1

Step 1 : Find the product

$$\begin{gathered} \frac{1}{2}\times \frac{2}{3}\times \frac{3}{8}=\frac{1}{8} \\ \text{And} \\ \frac{1}{7}\times \frac{2}{3}\times \frac{7}{8}=\frac{1}{3\times 4}=\frac{1}{12} \end{gathered}$$

Step 2 : Find the greater number

Take LCM of $\left(8,12\right)=24$

Now,

$$\begin{gathered} \frac{1}{8}=\frac{1\times 3}{8\times 3}=\frac{3}{24} \\ \frac{1}{12}=\frac{1\times 2}{12\times 2}=\frac{2}{24} \\ \because 3>2 \end{gathered}$$

So, $\frac{3}{24}>\frac{2}{24}$ [ In equivalent fractions, fractions with greater numerators are greater ]

Hence, the required answer is $\frac{1}{2}\times \frac{2}{3}\times \frac{7}{8}>\frac{1}{7}\times \frac{2}{3}\times \frac{7}{8}$