Question

Chef Johnson used 4 1/2 cups of flour to make 4 fruit cakes how many cups of flour are needed for 1 cake

Answer 1

let's firstly convert the mixed fraction to an improper fraction.

$\bf \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{flour}{cups}&\stackrel{fruit}{cake}\\ \cline{1-2}\\ \frac{9}{2}&4\\[1em] x&1 \end{array}\implies \cfrac{~~\frac{9}{2}~~}{x}=\cfrac{4}{1}\implies \cfrac{~~\frac{9}{2}~~}{\frac{x}{1}}=\cfrac{4}{1}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=4 \\\\\\ \cfrac{9}{2x}=4\implies 9=8x\implies \cfrac{9}{8}=x\implies 1\frac{1}{8}=x$