Chapter 7
Ratios, Rates, and Percents
Two bags of rice sit on the shelf. One is bigger, one is cheaper, and counting settles nothing. Subtracting does not settle it either: the question is not how far apart the two numbers are, but how they stand next to each other. Comparisons of that kind are what ratios are for. It sounds like a small change in how you read a pair of numbers, and the surprise is how much of ordinary arithmetic rests on it.
What You'll Explore
5 lessons.
- Ratios
Mix two cups of juice with three cups of water, then double both. Is it the same drink, and is it the same comparison? This lesson looks at what a comparison of two quantities actually records, what it leaves out, and how one total can be split so a comparison holds.
- Rates and Unit Rates
Twelve dollars for five pounds, or nineteen dollars for eight: which tag is the better deal? Eyeballing it is guesswork. This lesson takes up comparisons between quantities measured in different units, like money against weight or distance against time, and asks what makes two of them comparable.
- Proportions
Suppose a recipe serving four needs six eggs and ten people are coming. Three numbers are known, one is not, and the two comparisons have to match. This lesson is about what it means to say that two ratios are equal, and what such a statement lets you find.
- Percent
Seventeen out of twenty, or thirteen out of fifteen: which score is stronger? Comparing them means putting both on a common footing first. This lesson takes up the single scale that almost everyone already uses for that job, from shop windows to weather reports, and the questions it makes easy to ask.
- Percent Increase and Decrease
A price rises by ten percent and then falls by ten percent. Are you back where you started? This lesson follows what a percentage of change is measured against, and what happens when discounts, taxes, and tips are applied one after another.