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?

Given:

A number is subtracted from $\frac{1}{2}$ and the result is multiplied by $\frac{1}{2}$, we will get $\frac{1}{8}$.

To do:

We have to find the number.

Solution:

Let the number be $x$.

The number is subtracted from $\frac{1}{2}$.

So, we get,

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

The result is multiplied by $\frac{1}{2}$, so we get $\frac{1}{8}$.

This implies,

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

$\frac{1}{2} - x = \frac{1}{8}\times2$

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

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

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

$\frac{1\times 2}{2 \times 2} - \frac{1}{4} = x$    [LCM of 2, 4 is 4]

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

$\frac{1}{4} = x$

$x =\frac{1}{4} $

Therefore, the value of $x$ is $\frac{1}{4}$. 

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Updated on: 10-Oct-2022

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