Question

A piece of wire is of length $12\frac{3}{4}\mathrm{m}$. If it is cut into two pieces in such a way that the length of one piece is $5\frac{1}{4}\mathrm{m},$ what is the length of the other piece?

Answer 1

Let the length of second piece be x.

Total length of wire = Length of one piece + Length of second piece

$$\begin{gathered} 12\frac{3}{4}=5\frac{1}{4}+x \\ \Rightarrow \frac{(12\times 4)+3}{4}=\frac{(5\times 4)+1}{4}+x \\ \Rightarrow x=\frac{(12\times 4)+3}{4}-\frac{(5\times 4)+1}{4} \\ \Rightarrow x=\frac{51}{4}-\frac{21}{4}\iff \frac{30}{4} \\ \Rightarrow x=\frac{30}{4}\iff \frac{15}{2} \end{gathered}$$