Percentages
Percent questions show up constantly on the test — discounts, tax, interest, population growth. Master the one core idea here and you'll bank easy points fast.
| Change | Multiplier | Example on $200 |
|---|---|---|
| Increase 15% | × 1.15 | 200 × 1.15 = 230 |
| Decrease 15% | × 0.85 | 200 × 0.85 = 170 |
| Increase 100% | × 2.00 | 200 × 2 = 400 |
| Decrease 40% | × 0.60 | 200 × 0.60 = 120 |
Turn any percent change into a single multiplication.
| P | r | t | Interest |
|---|---|---|---|
| $2000 | 0.04 | 4 | $320 |
| $500 | 0.04 | 4 | $80 |
| $1500 | 0.06 | 2 | $180 |
Rate must be a decimal; the result is interest earned, not the total.
One trap to internalize now: the interest formula gives you interest earned, not the total. If a question asks for the final balance, add the interest back to the principal.
The whole topic comes down to three moves: convert percent to decimal, multiply, and decide whether you want the part, the change, or the total. Read the question to see which one it wants.
Check your understanding with a question from this topic:
$2000 is invested at a simple interest rate of 4% per year. How much interest is earned after 4 years?
Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).
Worked examples
A product originally costs $740. After a 15% price increase, what is the new price, in dollars?
$500 is invested at a simple interest rate of 4% per year. How much interest is earned after 4 years?
A shirt is on sale for $34, which is 15% off its original price. What was the original price, in dollars?
Common pitfalls
4% is 0.04, not 4. Plugging in 4 instead of 0.04 makes your answer 100 times too big. Always move the decimal two places left before multiplying.
P × r × t gives only the interest. If the question asks for the account balance or total amount, you must add the principal back: total = P + P×r×t.
If a sale price is 15% off and you want the original, don't add 15% back. The sale price is 85% of the original, so divide by 0.85 — adding 15% gives the wrong answer.
Percent change is always relative to the original value, not the new one. (new − old)/old, never divided by the new number.
Key takeaways
Convert percent to decimal by dividing by 100 (move decimal two places left) before doing any math.
Increase by p% → multiply by (1 + p/100); decrease by p% → multiply by (1 − p/100).
Simple interest = P × r × t, with r as a decimal; it gives interest only, not the total.
To reverse a percent change, divide by the multiplier instead of multiplying.
Percent change = (new − old) / old × 100, always relative to the original.
Watch & learn
Curated Khan Academy walkthroughs on Percentages. They're complementary to this lesson — watch one if a written explanation isn't clicking, or after to reinforce.
Try it yourself
5 practice questions on Percentages, drawn from the question bank. The tutor is one click away if you get stuck.