Question

If you subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, you get $\frac{1}{8}$.What is the number?

Answer 1

Step 1: Form the equation

Let the number be $x$.

According to the question,

$\left(x-\frac{1}{2}\right)\frac{1}{2}=\frac{1}{8}$

Step 2: Solve for $x$

Upon evaluating this equation we get,

$\left(x-\frac{1}{2}\right)\frac{1}{2}=\frac{1}{8}$

$\Rightarrow$ $x-\frac{1}{2}=\frac{2}{8}$

$\Rightarrow$ $\frac{2x-1}{2}=\frac{2}{8}$

$\Rightarrow$ $2x-1=\frac{4}{8}$

$\Rightarrow$ $2x-1=\frac{1}{2}$

$\Rightarrow$ $2x=1+\frac{1}{2}$

$\Rightarrow$ $2x=\frac{3}{2}$

$\Rightarrow$ $x=\frac{3}{4}$

Hence, the required number is $\frac{3}{4}$.