Question

An interior designer purchased 4 1/2 yard

Answer 1

Well, is just a matter of addition, namely 4  1/2 + 6  2/3 + 9  1/4.

now, let's change all mixed fractions firstly, to "improper" fractions, and proceed from there,

$\bf \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+}{1}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\\\ \stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} \\\\\\ \stackrel{mixed}{9\frac{1}{4}}\implies \cfrac{9\cdot 4+1}{}\implies \stackrel{improper}{\cfrac{37}{4}}\\\\ -------------------------------$

$\bf \cfrac{9}{2}+\cfrac{20}{3}+\cfrac{37}{4}\impliedby \textit{our LCD is clearly \underline{12}}\implies \cfrac{(6)9+(4)20+(3)37}{12} \\\\\\ \cfrac{245}{12}\implies 20\frac{5}{12}$