Question

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

• A. $\frac{30}{91}$
• B. $\frac{23}{30}$
• C. $\frac{71}{30}$
• D. $\frac{19}{30}$

Answer 1

The correct option is C $\frac{71}{30}$

Let the number to be added be $x$.

After adding the number $x$ to the given rational numbers the sum will result to 3.

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

(LCM of 2, 3 and 5 is 30)

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

$\Rightarrow \frac{15}{30}+\frac{10}{30}-\frac{6}{30}+x=3$

$\Rightarrow \frac{19}{30}+x=3$

$\Rightarrow x=3-\frac{19}{30}=\frac{3\times 30}{1\times 30}-\frac{19}{30}$

$\Rightarrow x=\frac{90-19}{30}=\frac{71}{30}$

The required number is $\frac{71}{30}.$

The sum of the rational numbers is 3 after adding $\frac{71}{30}$ to the given rational numbers.