Question

What number should be added to $(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$ to get $3?$

Answer 1

Let the required number be $x$

According to the question,

$(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})+x=3$

$\Rightarrow x=3-(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$

$=\frac{3}{1}-(\frac{1\times 15}{2\times 15}+\frac{1\times 10}{3\times 10}+\frac{1\times 6}{5\times 6})$

$=\frac{3\times 30}{1\times 30}-(\frac{15}{30}+\frac{10}{30}+\frac{6}{30})$

$=\frac{90}{30}-\left(\frac{15+10+6}{30}\right)$

$=\frac{90}{30}-\frac{31}{30}$

$=\frac{90-31}{30}$

$=\frac{59}{30}$

Hence, the required number is $\frac{59}{30}.$