Question

$\text{Choose the product from the given options}\text{for}\frac{3}{7}\times \frac{A}{B}\times \frac{B}{C}\text{, when}A=B\text{and}B<C$

• A. $\text{Product}=\frac{3}{7}$
• B. $\text{Product}<\frac{3}{7}$
• C. $\text{Product}>\frac{3}{7}$
• D. $\text{Cannot be determined}$

Answer 1

The correct option is B $\text{Product}<\frac{3}{7}$

$Given:A=B$

$\text{Consider,}\frac{3}{7}\times \frac{A}{B}\times \frac{B}{C}$

$⟹\frac{A}{B}=\frac{A}{A}$

$⟹\frac{3}{7}\times \frac{A}{B}=\frac{3}{7}\times \frac{A}{A}$

$\text{Now, when a fraction is multiplied by a}\text{fraction of the type}\frac{n}{n}\text{, the resulting}\text{product will be the same as the original}\text{fraction.}$

$\therefore \frac{3}{7}\times \frac{A}{A}=\frac{3}{7}$

$\text{So, the given expression can be rewritten}\text{as:}$

$\frac{3}{7}\times \frac{A}{B}\times \frac{B}{C}=\frac{3}{7}\times \frac{B}{C}$

$Given:B<C$

$⟹\frac{B}{C}<1$

$\text{When a fraction is multiplied by a fraction}\text{less than 1, the resulting product will}\text{be less than the original fraction.}$

$\therefore \frac{3}{7}\times \frac{B}{C}<\frac{3}{7}$

$⟹\frac{3}{7}\times \frac{A}{B}\times \frac{B}{C}<\frac{3}{7}$

$\text{Hence, the product is less than the original}\text{fraction}\frac{3}{7}$

$\therefore \text{The correct option is,}Product<\frac{3}{7}$