Question

2 1/4/6 2/3=d/10 2/3 The answer is 3 3/5.Please show work so I can understand how to solve.

Answer 1

`\bf \cfrac{2(1)/(4)}{6(2)/(3)}=\cfrac{d}{10(2)/(3)}\\\\ -----------------------------\\\\ \textit{now, let's convert those mixed fractions to}\\ \textit{fractions with only one top and bottom, or}\\ \textit{so-called`

`\bf -----------------------------\\\\ \cfrac{(9)/(4)}{(20)/(3)}=\cfrac{d}{(32)/(3)}\impliedby recall\to \cfrac{(a)/(b)}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c} \\\\ thus \\\\ \cfrac{(9)/(4)}{(20)/(3)}=\cfrac{d}{(32)/(3)}\implies \cfrac{(9)/(4)}{(20)/(3)}=\cfrac{(d)/(1)}{(32)/(3)}\implies \cfrac{9}{4}\cdot \cfrac{3}{20}=\cfrac{d}{1}\cdot \cfrac{3}{32} \\\\`


`\bf \cfrac{27}{80}=\cfrac{3d}{32}\implies \cfrac{27\cdot 32}{80\cdot 3}=d\impliedby cross-multiplying \\\\\\ \cfrac{864}{240}=d\implies \boxed{\cfrac{18}{5}}=d \\\\\\\\ \boxed{3(3)/(5)}\iff \cfrac{3\cdot 5+3}{5}\implies \cfrac{18}{5}`