Question

When a rational number is subtracted from $1\frac{3}{4}$ , it yields $\frac{1}{12}$ .Then, the rational number will be .

• A. $\frac{3}{5}$
• B. $1\frac{2}{3}$
• C. $-\frac{5}{3}$

Answer 1

The correct option is B $1\frac{2}{3}$

Let the rational number be x.

According to the given situation,
$1\frac{3}{4}-x=\frac{1}{12}$
$\Rightarrow$ $\frac{7}{4}-x=\frac{1}{12}$
$\Rightarrow$ $\frac{7}{4}-x-\frac{7}{4}=\frac{1}{12}-\frac{7}{4}$
($\because$ LCM 0f 12 and 4 is 12 )
$\Rightarrow$ $-x=\frac{1-21}{12}$
$\Rightarrow$ $-x=\frac{-20}{12}$
$\Rightarrow$ $x=\frac{20}{12}$
$\Rightarrow$ $x=\frac{5}{3}$
$\Rightarrow$ $x=1\frac{2}{3}$

Therefore, the rational number is $1\frac{2}{3}$.