Question

A recipe for 1 batch of cookies calls for 4 2/3 cups of walnuts . Damian wants to make 1 1/4 of a batch. How many cups of walnuts does he need?

Answer 1

let's firstly convert the mixed fractions to improper fractions and then proceed.

`\stackrel{mixed}{4(2)/(3)}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}}~\hfill \stackrel{mixed}{1(1)/(4)}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} batches&cups\\ \cline{1-2} 1&(14)/(3)\\[1em] (5)/(4)&x \end{array}\implies \cfrac{1}{~~ (5)/(4)~~}=\cfrac{~~ (14)/(3)~~}{x}\implies \cfrac{(1)/(1)}{~~ (5)/(4)~~}=\cfrac{~~ (14)/(3)~~}{(x)/(1)}\implies \cfrac{1}{1}\cdot \cfrac{4}{5}=\cfrac{14}{3}\cdot \cfrac{1}{x} \\\\\\ \cfrac{4}{5}=\cfrac{14}{3x}\implies 12x=70\implies x=\cfrac{70}{12}\implies x=\cfrac{35}{6}\implies x=5(5)/(6)`