Question

What is the width of the rectangle? Area: 24 3/4 Length: 6 1/2 Width:

Answer 1

let's firstly convert the mixed fractions to improper fractions.

$\bf \stackrel{mixed}{24\frac{3}{4}}\implies \cfrac{24\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{99}{4}}~\hfill \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{area of a rectangle}}{A=Lw}\implies \cfrac{A}{L}=w~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\frac{13}{2}\\\\ A=\frac{99}{4} \end{cases}\implies \cfrac{~~\frac{99}{4}~~}{\frac{13}{2}}=w \\\\\\ \cfrac{99}{4}\cdot \cfrac{2}{13}=w\implies \cfrac{99}{13}\cdot \cfrac{2}{4}=w\implies \cfrac{99}{13}\cdot \cfrac{1}{2}=w\implies \cfrac{99}{26}=w\implies 3\frac{21}{26}=w$