Percent: Every Number Is 100 Squares
Shade the grid to see the part — then rescale to any quantity you like.
The 100-square grid — your mental anchor
A 10×10 grid has exactly 100 squares. Shade 40 of them — you've shown 40%. The fraction is 40/100 = 2/5; the decimal is 0.40. These are three ways to write the exact same proportion.
Now apply that proportion to a real quantity. 40% of 80 students = 0.40 × 80 = 32 students. The percent tells you the proportion; the actual quantity tells you what you're proportioning.
| Percent | Fraction | Decimal |
|---|---|---|
| 25% | 25/100 = 1/4 | 0.25 |
| 50% | 50/100 = 1/2 | 0.50 |
| 75% | 75/100 = 3/4 | 0.75 |
| 1% | 1/100 | 0.01 |
| 100% | 1/1 (the whole) | 1.00 |
| 150% | 3/2 | 1.50 |
Decimal method (fastest): move the percent sign and divide by 100 → multiply. 35% of 60 = 0.35 × 60 = 21.
Fraction method (more intuitive): 35% = 35/100 = 7/20. Then 7/20 × 60 = 420/20 = 21.
Both give 21. Use whichever feels natural; the decimal method generalises better to a calculator.
150% of 80 is more than 80 — it means one whole (100%) plus an extra half (50%): 1.50 × 80 = 120. Percents above 100% arise in real life: 'Sales increased by 150%' means more than doubled.
Percents below 1% are also valid: 0.5% = 0.005 as a decimal, and 0.5% of 200 = 1.
- Convert: 35% = 0.35.
- Multiply: 0.35 × 120 = 42.
- Write as a fraction: 18/24.
- Convert to decimal: 18 ÷ 24 = 0.75.
- Convert to percent: 0.75 × 100 = 75%.
Check your understanding
- Percent means 'per hundred' — the 10×10 grid anchors this visually.
- To find a percent of a number: convert the percent to a decimal (÷ 100), then multiply.
- To find what percent A is of B: compute A ÷ B, then multiply by 100.
- Percents above 100% represent more than the whole; percents below 1% are still valid.
- Percent, decimal, and fraction are three forms of the same proportion.