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

Given :

The given numbers are $(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$ and $3$.

To do :

We have to find the number that should be added to $(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$ to get $3$.

Solution :

Let the number to be added to $(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$ to get $3$ be $x$.

This implies,

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

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

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

$x=3-\frac{31}{30}$

$x = \frac{3(30)-31}{30}$

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

$x=\frac{59}{30}$

The number to be added to $(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})$ to get $3$ is $\frac{59}{30}$.      

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Updated on: 10-Oct-2022

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