Percentages Using Arithmetic
A percentage is simply a fraction out of 100. Every percentage problem can be solved with basic arithmetic — multiplication and division.
This page pulls together the core arithmetic behind every percentage skill on this site — finding a percentage of an amount, increasing or decreasing by a percentage, and working backwards to an original value — into one quick-reference toolkit. Whichever context a percentage problem shows up in (a discount, a tax, a population change), the underlying arithmetic is always one of these same few operations: multiply by the decimal equivalent, multiply by a growth/shrink multiplier, or divide to reverse one of those steps.
Finding a Percentage of an Amount
15% of 200 = 0.15 × 200 = 30
35% of 480 = 480 × 35 ÷ 100 = 168
Percentage Increase and Decrease
Increase £250 by 20%: 250 × 1.20 = £300
Decrease £80 by 15%: 80 × 0.85 = £68
Converting Fractions and Decimals to Percentages
| Fraction/Decimal | Percentage |
|---|---|
| 1/4 | 25% |
| 3/5 | 60% |
| 0.375 | 37.5% |
Finding the Original Value (Reverse Percentage)
After a 20% increase the price is £120. Original = 120 ÷ 1.20 = £100
Key Takeaways
- Percentage = fraction of 100.
- Multiply by the decimal equivalent: 35% = 0.35.
- Increase: multiply by (1 + rate); Decrease: multiply by (1 − rate).
- Reverse percentage: divide by the multiplier.
Practice: Mixed Percentage Review
Percentage Review