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?

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Solution

## Let the length of second piece be x. Total length of wire = Length of one piece + Length of second piece $12\frac{3}{4}=5\frac{1}{4}+x\phantom{\rule{0ex}{0ex}}⇒\frac{\left(12×4\right)+3}{4}=\frac{\left(5×4\right)+1}{4}+x\phantom{\rule{0ex}{0ex}}⇒x=\frac{\left(12×4\right)+3}{4}-\frac{\left(5×4\right)+1}{4}\phantom{\rule{0ex}{0ex}}⇒x=\frac{51}{4}-\frac{21}{4}⇔\frac{30}{4}\phantom{\rule{0ex}{0ex}}⇒x=\frac{30}{4}⇔\frac{15}{2}$

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