Percent
Eighteen of 25 seats are full on one ride and 34 of 50 on another. How do you compare parts of wholes that are not the same size?
Where you are 8 inside
What this area is about
A percent is a rate per hundred: p\% means p for every 100, so \displaystyle p\% = \frac{p}{100}. Measuring every part against the same 100 lets parts of different wholes sit side by side. Almost every question here ties three numbers together: part = percent \times whole.
How these fit together
The idea. What percent means defines it as a ratio whose second amount is always 100. Converting among fractions, decimals and percents renames one number in all three forms, and percents above 100 and below 1 cover a comparison larger than the whole or a part too small for a whole percent.
Finding the numbers. Benchmark percents such as 10\% and 50\% work in the head and give estimates. Finding a percent of a quantity multiplies by the percent as a decimal, and the three percent questions solve for whichever of part, percent or whole is missing.
Uses. Percent change measures a rise or fall against a reference amount, usually the start. Percent in money situations covers discounts, tax, tips, markup and interest.
A path through it
What percent means first, then converting. A percent of a quantity follows converting; after it come percents above 100 and below 1, and the three percent questions. Percent change needs all three of those, and money situations come last. Benchmark percents fit any time after the first lesson and before money.
Sampling and study design assumes percent.