Respuesta :
[tex]\bf \cfrac{2\frac{1}{4}}{6\frac{2}{3}}=\cfrac{d}{10\frac{2}{3}}\\\\
-----------------------------\\\\
\textit{now, let's convert those mixed fractions to}\\
\textit{fractions with only one top and bottom, or}\\
\textit{so-called "improper fraction"s}
\\\\
\begin{cases}
2\frac{1}{4}\implies \cfrac{2\cdot 4+1}{4}\implies &\cfrac{9}{4}
\\\\
6\frac{2}{3}\implies \cfrac{6\cdot 3+2}{3}\implies &\cfrac{20}{3}
\\\\
10\frac{2}{3}\implies \cfrac{10\cdot 3+2}{3}\implies &\cfrac{32}{3}
\end{cases}\\\\
[/tex]
[tex]\bf -----------------------------\\\\ \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{d}{\frac{32}{3}}\impliedby recall\to \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c} \\\\ thus \\\\ \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{d}{\frac{32}{3}}\implies \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{\frac{d}{1}}{\frac{32}{3}}\implies \cfrac{9}{4}\cdot \cfrac{3}{20}=\cfrac{d}{1}\cdot \cfrac{3}{32} \\\\ [/tex]
[tex]\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\frac{3}{5}}\iff \cfrac{3\cdot 5+3}{5}\implies \cfrac{18}{5}[/tex]
[tex]\bf -----------------------------\\\\ \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{d}{\frac{32}{3}}\impliedby recall\to \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c} \\\\ thus \\\\ \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{d}{\frac{32}{3}}\implies \cfrac{\frac{9}{4}}{\frac{20}{3}}=\cfrac{\frac{d}{1}}{\frac{32}{3}}\implies \cfrac{9}{4}\cdot \cfrac{3}{20}=\cfrac{d}{1}\cdot \cfrac{3}{32} \\\\ [/tex]
[tex]\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\frac{3}{5}}\iff \cfrac{3\cdot 5+3}{5}\implies \cfrac{18}{5}[/tex]
