Question

A recipe for 1 batch of cookies calls for 1/2 of a cup of raisins. Diego has 2 cups of raisins. How many batches can he make?

Answer 1

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