Percentages
Core Idea
A percent is just a ratio out of 100. Every percentage problem — whether it involves discounts, growth, or converting between forms — comes back to that single idea.
Understanding
"Percent" literally means "per hundred." Writing 40% is the same as writing
On the SAT, percentages show up in two main flavors. The first is straightforward calculation: find 15% of a number, or figure out what percent one quantity is of another. The second — and the one that trips people up more often — is percent change: prices going up, populations going down, values compounding over time.
The key mechanical skill is converting fluently between percent, decimal, and fraction forms so you can plug into whatever equation the problem demands. The key conceptual skill is knowing when to multiply by the percent itself versus the growth factor
Most errors on percent problems aren't arithmetic mistakes. They come from mixing up the base — taking a percent of the wrong number, or applying an increase to an already-increased value. Staying clear on what quantity is 100% will prevent the majority of those mistakes.