Question

James has to solve the given expression in the easiest way. The approach he should take is

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

Answer 1

The correct option is C Approach 3

Calculating the expression through each approach, we find:

$Approach1:$

$(\frac{2}{3}\times \frac{4}{13})\times \frac{9}{2}$

Multiply the first two terms:

$\frac{2}{3}\times \frac{4}{13}=\frac{2\times 4}{3\times 13}=\frac{8}{39}$

Now,

$\frac{8}{39}\times \frac{9}{2}=\frac{8\times 9}{39\times 2}=\frac{72}{78}=\frac{72÷6}{78÷6}=\frac{12}{13}$

$Approach2:$

$(\frac{4}{13}\times \frac{9}{2})\times \frac{2}{3}$

Multiply first two terms:

$\frac{4}{13}\times \frac{9}{2}=\frac{4\times 9}{13\times 2}=\frac{36}{26}=\frac{36÷2}{26÷2}=\frac{18}{13}$

Now,

$\frac{18}{13}\times \frac{2}{3}=\frac{18\times 2}{13\times 3}=\frac{36}{39}=\frac{36÷3}{39÷3}=\frac{12}{13}$

$Approach3:$

$(\frac{2}{3}\times \frac{9}{2})\times \frac{4}{13}$

Multiply first two terms:

$\frac{2}{3}\times \frac{9}{2}=\frac{2\times 9}{3\times 2}=\frac{18}{6}=\frac{3}{1}$

Now,

$\frac{3}{1}\times \frac{4}{13}=\frac{12}{13}$

$\therefore \text{The easiest approach to calculate the}$$\text{given expression is}approach3.$