MathBench > Miscellaneous

Tricks with Division

Section 2: Proportions and Percents

Proportions and Percents: Parts of the Whole

It’s natural with the pound cake example to want to ask, how much of the total recipe is butter? And naturally mathematicians have come up with a way of doing this: use a proportion.

Basically you’re asking “what’s the ratio of the part (butter) to the whole (all the ingredients). So…

butter : (butter + eggs + flour + sugar)

= 12 : (12 + 10 + 13 + 21)

= 12 : 56

= 0.21

In other words, out of one whole cake, 0.21, or about a fifth, is butter. That’s a proportion, since it compares the amount of butter to ONE cake. However, it's often easier to express this as a percentage. Essentially a percentage says, if I took the cake and divided it into 100 mini-pieces, how many of those mini-pieces would consist of butter? So, multiply the proportion above (0.21) by 100.


So, two ways to find the relationship between the part and the whole:

proportion: divide the “part” number by the “whole” number

percent: do the above, then multiply by 100

Quick Practice:

What is the % of each ingredient in the lowfat (56 oz) cake?

12 oz corn-oil butter

10 oz eggs

13 oz flour

21 oz sugar