Question

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

Answer 1

Hint: We will first consider the given information and accordingly form the equation to solve the question. We will first let the number as $$x$$. We will first subtract $${\displaystyle \frac{1}{2}}$$ from $$x$$ and multiply the same expression by $${\displaystyle \frac{1}{2}}$$ and put it equal to $${\displaystyle \frac{1}{8}}$$. This will make an equation so, we need to solve the obtained equation for $$x$$.

Complete step-by-step answer:
We will first let the number as $$x$$.
Now, we will follow the given statement and form an equation that is we need to subtract $${\displaystyle \frac{1}{2}}$$ from the number $$x$$ and then multiply the whole expression by $${\displaystyle \frac{1}{2}}$$ and put it equal to $${\displaystyle \frac{1}{8}}$$.
Thus, we get,
$$\Rightarrow \left(x-{\displaystyle \frac{1}{2}}\right){\displaystyle \frac{1}{2}}={\displaystyle \frac{1}{8}}$$
Now, we will simplify the equation by multiplying both the sides by 2.
$$\begin{gathered} \Rightarrow \left(x-{\displaystyle \frac{1}{2}}\right){\displaystyle \frac{1}{2}}\times 2={\displaystyle \frac{1}{8}}\times 2 \\ \Rightarrow x-{\displaystyle \frac{1}{2}}={\displaystyle \frac{1}{4}} \end{gathered}$$
Next, we will add $${\displaystyle \frac{1}{2}}$$ on both the sides of the equation, and simplify the right-hand side by taking the L.C.M.
Thus, we get,
$$\begin{gathered} \Rightarrow x-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}={\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{2}} \\ \Rightarrow x={\displaystyle \frac{1+2}{4}} \\ \Rightarrow x={\displaystyle \frac{3}{4}} \end{gathered}$$
Hence, we can conclude that the number is obtained as $${\displaystyle \frac{3}{4}}$$.

Note: Form the equation carefully as it is the first step of solving the equation. While doing simplification do it properly so that there may not arise any calculation error. Take the L.C.M. between the numbers carefully. We can also verify the value by substituting it in the equation we have formed from the question.