Percentages
Working with percentages
- Percentage of an amount: 15% of 80 = 0.15 × 80 = 12.
- One amount as a % of another: 18 out of 25 = $\tfrac{18}{25}\times100\% = 72\%$.
- Percentage change $= \dfrac{\text{change}}{\text{original}}\times100\%$. A multiplier of 1.15 adds 15%; 0.85 removes it.
Practice
What is 15% of 80?
0.15 × 80 = 12.
Practice
A price rises from 40 to 50. What is the percentage increase?
change/original × 100% = 10/40 × 100% = 25%.
Interest & reverse %
- Simple interest: $I = \dfrac{Prt}{100}$. Compound: final $= P\left(1+\tfrac{r}{100}\right)^t$.
- Reverse percentage: given the amount after a change, divide by the multiplier. 60 after a 20% rise → 60 ÷ 1.2 = 50.
Practice
A coat costs 60 after a 20% increase. What was the original price?
60 is 120% of the original, so 60 ÷ 1.2 = 50.
You've got it
Key idea
- 15% of 80 = 12; percentage change $= \dfrac{\text{change}}{\text{original}}\times100\%$
- compound value $= P(1 + r/100)^t$
- reverse %: divide by the multiplier (don't just subtract)