Question

It takes 2/3 cup of ketchup to make a batch of barbeque sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?

Answer 1

Explanation:

to see how often one quantity fits into another quantity (and how much remains), we use division.

we divide 9 cups of ketchup by 2/3 (the amount needed to make one batch of barbecue sauce) :

9 / 2/3 = 9/1 / 2/3 = (9×3) / (1×2) = 27/2 = 13 1/2

as you remember,

a/b / c/d = (ad)/(bc)

so, she makes 13 whole batches of barbecue sauce.

for these 13 batches she uses 13 × 2/3 = 26/3 cups of ketchup.

from the original 9 cups = (3×9)/3 = 27/3 cups of ketchup, there is therefore 27/3 - 26/3 = 1/3 cup remaining.