Question

A cookie recipe requires 4 2/3 cups of flour. If a person only wanted to make 3/4 of a batch, how many cups of flour would they need? (Do not add the label)

Answer 1

`\begin{array}{ccll} \stackrel{recipe}{batch}&\stackrel{recipe}{flour}\\ \cline{1-2} 1&4(2)/(3)\\[1em] (3)/(4)&f \end{array}\implies \cfrac{1}{ ~~ (3)/(4)~~ }~~ = ~~\cfrac{ ~~ 4(2)/(3) ~~ }{f}\implies \cfrac{4}{3}~~ = ~~\cfrac{ ~~ (4\cdot 3+2)/(3)~~ }{f}\implies \cfrac{4}{3}=\cfrac{ ~~ (14)/(3) ~~ }{f} \\\\\\ \cfrac{4}{3}=\cfrac{14}{3f}\implies 12f=42\implies f=\cfrac{42}{12}\implies f=\cfrac{7}{2}\implies f=3(1)/(2)`