Question

Explain the process to solve the equation. Use proper vocabulary in your explanation. $\frac{1}{4}x=\frac{5}{8}$

Answer 1

Eliminate the denominator from the left hand side:

• It can be observed that in the given equation, if the coefficient of the variable eliminates, then the solution of the equation will appear.
• In order to get rid of $4$ from the denominator, multiply both sides of the given equation by $4$.

$$\begin{gathered} \begin{array}{rcl}4\times \frac{1\times x}{4}& =& \frac{5\times 4}{8}\\ & \Rightarrow & 4\times \frac{1\times x}{4}=\frac{5\times 4}{8}\\ & \Rightarrow & 1x=\frac{20}{8}\end{array}\left[\mathrm{simplify}\mathrm{the}\mathrm{obatined}\mathrm{result}\right] \\ \Rightarrow x=\frac{5}{2} \end{gathered}$$

Hence, the simplified value of $x$ is $\frac{5}{2}$.