Question

A cookie recipe calls for 1 1/2 cups of flour for every 1/3 cup of sugar. Could you increase the recipe proportionately by using 12 cups of flour and 2 cups of sugar?

Answer 1

we certainly could do so IF only IF the proportion of 12 and 2 are at the same ratio as 1½ and 1/3, namely if both yield the same fraction, let's see, and firstly converting the mixed fraction to improper.

`\bf \cfrac{12}{2}=\cfrac{~~1(1)/(2)~~}{(1)/(3)}\implies 6=\cfrac{~~(1\cdot 2+1)/(2)~~}{(1)/(3)}\implies 6=\cfrac{~~(3)/(2)~~}{(1)/(3)}\implies 6=\cfrac{3}{2}\cdot \cfrac{3}{1}\implies 6\\e \cfrac{9}{2}~~\bigotimes`