How to use it
This page has five small calculators, one for each kind of percent question you're likely to meet. Fill in the boxes for the one you need and the answer appears below it, with the reasoning spelled out. Decimals (12.5) and fractions (1/3) are fine.
The ideas behind them
- Percent of a number. Percent means “per hundred”, so 15% of 80 is \(\frac{15}{100} \cdot 80 = 12\).
- What percent is it? Divide the part by the whole and multiply by 100. Getting 18 out of 24 on a quiz is \(\frac{18}{24} \cdot 100 = 75\%\).
- Discounts and markups. A 20% discount on a 60-dollar jacket takes off 12 dollars, so you pay 48 dollars. The one-step shortcut is to multiply by \(0.8\): taking off 20% leaves 80%. Sales tax works the same way in the other direction, multiplying by \(1.07\) for a 7% tax.
- Percent change. Compare the change with the original value. Going from 50 to 65 is a change of 15, which is a 30% increase over 50.
Back-to-back percents
A 20% increase followed by a 20% decrease does not bring you back to where you started. 100 becomes 120, and 20% of 120 is 24, so you end at 96. The second percent is taken of a different number. Run both steps in the “Discount or markup” calculator and watch it happen.
Proportions
In the last calculator, fill in three of the four boxes and leave the unknown one blank. A proportion \(\frac{a}{b} = \frac{c}{d}\) has equal cross products, \(a \cdot d = b \cdot c\), and that's all you need to find the missing value. It's how you scale a recipe or work out unit prices: if 3 pounds of apples cost 4 dollars, then 15 dollars buys \(x\) pounds, where \(\frac{3}{4} = \frac{x}{15}\).