Question

$\frac{4}{9}\times \frac{7}{17}\times \frac{9}{2}$

The best approach to calculate the product above is

• A. Approach 1
• B. Approach 2
• C. Approach 3

Answer 1

The correct option is B Approach 2

$\text{Calculating the product through each}\text{approach, we find:}$

$Approach1:$

$(\frac{4}{9}\times \frac{7}{17})\times \frac{9}{2}$

$=\left(\frac{4\times 7}{9\times 17}\right)\times \frac{9}{2}$

$=\frac{28}{153}\times \frac{9}{2}$

$=\frac{28\times 9}{153\times 2}$

$=\frac{14\times 1}{17\times 1}$

$=\frac{14}{17}$

$Approach2:$

$(\frac{4}{9}\times \frac{9}{2})\times \frac{7}{17}$

$=\frac{4\times 9}{9\times 2}\times \frac{7}{17}$

$=2\times \frac{7}{17}$

$=\frac{2\times 7}{1\times 17}$

$=\frac{14}{17}$

$Approach3:$

$(\frac{7}{17}\times \frac{9}{2})\times \frac{4}{9}$

$=\frac{7\times 9}{17\times 2}\times \frac{4}{9}$

$=\frac{63}{34}\times \frac{4}{9}$

$=\frac{63\times 4}{34\times 9}$

$=\frac{7\times 2}{17\times 1}$

$=\frac{14}{17}$

$\text{In}approach2\text{the numerator and the}\text{denominator cancel out easily.}$

$\therefore \text{The best approach to calculate the}\text{product is}approach2.$