Question

A baker has 10 cups of sugar to make cookies. Each batch calls for 1 1/3 cups of sugar.

How many batches of cookies can he make?

Answer 1

`\bf \textit{he can make }10/ 1(1)/(3)\qquad or\qquad \cfrac{10}{1(1)/(3)} \\\\\\ 1(1)/(3)\implies \cfrac{1\cdot 3+1}{3}\implies \cfrac{4}{3}\\\\ -----------------------------\\\\ \cfrac{(a)/(b)}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus\\\\ -----------------------------\\\\`


`\bf \cfrac{10}{(4)/(3)}\implies \cfrac{(10)/(1)}{(4)/(3)}\implies \cfrac{10}{1}\cdot \cfrac{3}{4}\implies \cfrac{30}{4}\implies \cfrac{15}{2}\implies \boxed{7(1)/(2)} \\\\\\ because\implies \cfrac{7\cdot 2+1}{2}\implies \cfrac{15}{2}`