Question

What should be added to the sum of $\frac{3}{7}$ and thrice of $-\frac{6}{7}$ to get $\frac{17}{13}$.

Answer 1

First find the some of $\frac{3}{7}$ and thrice of $-\frac{6}{7}$.

Thrice of $-\frac{6}{7}=3\times (-\frac{6}{7})-\frac{18}{7}$

Now,

Sum of $\frac{3}{7}$ and Thrice of $-\frac{6}{7}$

$=\frac{3}{7}+(-\frac{18}{7})$

$=\frac{3}{7}-\frac{18}{7}$

$=\frac{3-18}{7}$

$=\frac{-15}{7}$

Let $x$ be the number to be added to get $\frac{17}{13}$.

$\Rightarrow x+\frac{-15}{7}=\frac{17}{13}$

$\Rightarrow x=\frac{17}{13}-\frac{-15}{7}$

Since, the LCM of $13$ and $7$ is $13\times 7=91$.

$\Rightarrow x=(\frac{17}{13}\times \frac{7}{7})-(\frac{-15}{7}\times \frac{13}{13})$

$\Rightarrow x=\frac{119}{91}+\frac{195}{91}$

$\Rightarrow x=\frac{119+195}{91}$

$\Rightarrow x=\frac{314}{91}$

$\Rightarrow x=3\frac{41}{91}$

Therefore, the required number is $3\frac{41}{91}$.