1. **Understanding Percentages** A percentage is a way to express a number as a fraction of 100. The symbol for percentage is **%**. 2. **Basic Definition** If you have a number $x$, then $x\%$ means $\frac{x}{100}$. 3. **Converting a Percentage to a Decimal** To convert a percentage to a decimal, divide by 100. Example: $25\% = \frac{25}{100} = 0.25$ 4. **Converting a Decimal to a Percentage** To convert a decimal to a percentage, multiply by 100. Example: $0.75 = 0.75 \times 100 = 75\%$ 5. **Finding a Percentage of a Number** To find $p\%$ of a number $N$, use the formula: $$\text{Percentage of } N = \frac{p}{100} \times N$$ Example: Find 20% of 50. $$= \frac{20}{100} \times 50 = 0.2 \times 50 = 10$$ 6. **Increasing a Number by a Percentage** To increase a number $N$ by $p\%$, calculate: $$N + \frac{p}{100} \times N = N \times \left(1 + \frac{p}{100}\right)$$ Example: Increase 80 by 15%. $$= 80 \times \left(1 + \frac{15}{100}\right) = 80 \times 1.15 = 92$$ 7. **Decreasing a Number by a Percentage** To decrease a number $N$ by $p\%$, calculate: $$N - \frac{p}{100} \times N = N \times \left(1 - \frac{p}{100}\right)$$ Example: Decrease 60 by 25%. $$= 60 \times \left(1 - \frac{25}{100}\right) = 60 \times 0.75 = 45$$ 8. **Percentage Change** The percentage change from an original value $O$ to a new value $N$ is: $$\text{Percentage Change} = \frac{N - O}{O} \times 100\%$$ Example: Original price is 50, new price is 65. $$= \frac{65 - 50}{50} \times 100 = \frac{15}{50} \times 100 = 30\%$$ increase. These steps cover the basics of percentages with clear examples to help understand and apply the concept.