Francine uses
\[\dfrac{2}3\] cup of pineapple juice for every
\[\dfrac{1}3\] cup of orange juice to make a smoothie.
Enter the number of cups of pineapple juice Francine uses for
\[1\] cup of orange juice.
If Francine uses \(\frac{2}{3}\) cup of pineapple juice for every \(\frac{1}{3}\) cup of orange juice, to find out how many cups of pineapple juice she uses for \(1\) cup of orange juice, we can set up a proportion or simply calculate it by seeing how many \(\frac{1}{3}\) cups are in \(1\) cup of orange juice.
Since \(1\) cup is made up of three \(\frac{1}{3}\) cups (\(1 = \frac{1}{3} + \frac{1}{3} + \frac{1}{3}\)), and for every \(\frac{1}{3}\) cup of orange juice she uses \(\frac{2}{3}\) cup of pineapple juice, we just multiply the amount of pineapple juice used for \(\frac{1}{3}\) cup of orange juice by 3.
\[
\left(\frac{2}{3}\right) \times 3 = \frac{2}{3} \times \frac{3}{1} = \frac{2 \times 3}{3 \times 1} = \frac{6}{3} = 2
\]
So, Francine uses \(2\) cups of pineapple juice for \(1\) cup of orange juice.