Table of Contents

• Prequiz
• 1: Three tricks division can do
• Section 1: Ratios and Fractions
• 2: Finding Ratios
• 3: More uses for Ratios
• Section 2: Proportions and Percents
• 4: Proportions and Percents: Parts of the Whole
• 5: Absolute amounts from percents
• 6: Parts and wholes
• Section 3: Percent Change
• 7: Measuring how things change
• 8: Percent Change is not a direct comparison
• 9: Units, units, units
• Section 4: Biology
• 10: What's in your milk?
• 11: An experiment

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