Ratios deal with proportions. By saying the ratio of oatmeal to raisins is 8 to 7 (or 8:7 or 8/7) it means for every 8 parts oatmeal, we need 7 parts raisins. so a "whole" is made up of 8 + 7 = 15 parts in all.

if we wrote the amount of oatmeal as a fraction of the whole, it would be 8/15. similarly, if we wrote the amount of raisins as a fraction of the whole, we would write 7/15.

now let the number of cups of raisins needed be r. we must have that:

cups

an alternative meathod would be to let the whole be x, since the fraction of the whole that is oatmeal is 8/15 we must have:

Let be the cups of raisins needed. Since the fraction of the whole that is raisins is 7/15, we must have

cups