Decimals and Fractions Practice Test 1

Let the numerator be x and the denominator be y
Then, ${\left(\mathit{x}+\mathit{y}\right)}^2=289$
$\Rightarrow \mathit{x}+\mathit{y}=17$ …(1)
Again, $\frac{3\mathit{x}+1}{2\mathit{y}-2}=\frac{2}{1}$
$3\mathit{x}+1=4\mathit{y}-1$
$3\mathit{x}-4\mathit{y}=-4-1$
$3\mathit{x}-4\mathit{y}=-5$ …(2)
Multiplying equation (1) by 3,
$3\mathit{x}+3\mathit{y}=51$ ....(3)
From equation (2) and (3), we get
$7\mathit{y}=56\Rightarrow \mathit{y}=8$
$\Rightarrow \mathit{x}=9$
So, the required fraction $=\frac{9}{8}.$