Question

What should be subtracted from $\frac{5}{9}$ to get $\frac{9}{5}$ ?

Answer 1

Step 1: Finding equations by using given conditions

Let, the required number be x.

According to the question,

Subtract x from $\frac{5}{9}$ to get $\frac{9}{5}$.

i.e., $\frac{5}{9}-x=\frac{9}{5}----------\left(i\right)$

Step 2: Solving equation to get required number

From e.q., (i) $x=\frac{5}{9}-\frac{9}{5}$

$=\frac{5\times 5}{9\times 5}-\frac{9\times 9}{5\times 9}$

$[\because LCMof5and9=5\times 9=45]$

$=\frac{25}{45}-\frac{81}{45}=\frac{25-81}{45}=\frac{-56}{45}$

Hence, $\frac{-56}{45}$ should be subtracted from $\frac{5}{9}toget\frac{9}{5}$.