Question

$\text{Calculate the value of}A\text{and}B\text{from the given}\text{expression:}$

$A\times B=\frac{8}{9}$

• A. $A=\frac{14}{5};B=\frac{15}{7}$
• B. $A=\frac{15}{9};B=\frac{3}{5}$
• C. $A=\frac{15}{9};B=\frac{4}{5}$
• D. $A=\frac{14}{9};B=\frac{4}{7}$

Answer 1

The correct option is D $A=\frac{14}{9};B=\frac{4}{7}$

$\text{Calculating the product}A\times B\text{for each}\text{case, we get:}$

$Case1:A=\frac{15}{9};B=\frac{4}{5}$

$A\times B=\frac{15}{9}\times \frac{4}{5}$

$=\frac{15}{9}\times \frac{4}{5}$

$=\frac{1}{3}\times \frac{4}{1}$

$=\frac{1\times 4}{3\times 1}$

$=\frac{4}{3}$

$Case2:A=\frac{14}{9};B=\frac{4}{7}$

$A\times B=\frac{14}{9}\times \frac{4}{7}$

$=\frac{14}{9}\times \frac{4}{7}$

$=\frac{2}{9}\times \frac{4}{1}$

$=\frac{2\times 4}{9\times 1}$

$=\frac{8}{9}$

$Case3:A=\frac{14}{5};B=\frac{15}{7}$

$A\times B=\frac{14}{5}\times \frac{15}{7}$

$=\frac{14}{5}\times \frac{15}{7}$

$=\frac{2}{1}\times \frac{3}{1}$

$=\frac{2\times 3}{1\times 1}$

​​​​​​​$=\frac{6}{1}=6$

$Case4:A=\frac{15}{9};B=\frac{3}{5}$

$A\times B=\frac{15}{9}\times \frac{3}{5}$

$=\frac{15}{9}\times \frac{3}{5}$

$=\frac{3}{3}\times \frac{1}{1}$

$=\frac{3\times 1}{3\times 1}$

​​​​​​​$=\frac{3}{3}$

​​​​​​​$=\frac{1}{1}=1$

$\therefore \text{Out of the four cases, the only case}\text{that gives}A\times B=\frac{8}{9}\text{is}case2\text{, where}A=\frac{14}{9};B=\frac{4}{7}$