how to find percentage of a number
To find the percentage of a number, you always use the same basic idea: a percentage is “how many out of 100.”
Core idea in one line
Percentage of a number=partwhole×100\text{Percentage of a number}=\frac{\text{part}}{\text{whole}}\times 100Percentage of a number=wholepart×100
If you already know the percentage you want (like “20% of 150”), you typically use:
Result=percentage100×number\text{Result}=\frac{\text{percentage}}{100}\times \text{number}Result=100percentage×number
Mini‑section 1: When you know part and whole
Use this when you want to know “What percent is this part of the total?”
- Formula: percent=partwhole×100\text{percent}=\dfrac{\text{part}}{\text{whole}}\times 100percent=wholepart×100.
- Example: In a class there are 26 boys and 24 girls, so 50 students total. 2650×100=52%\dfrac{26}{50}\times 100=52%5026×100=52%. That means 52% of the class are boys.
Think of it as: “part ÷ whole, then scale it up to a hundred.”
Mini‑section 2: When you know the percent and want the part
This is the classic “find percentage of a number” question: “What is 18% of 250?”
You can do it in two popular ways:
- Convert percent to decimal and multiply
- Convert 18% → 0.18 (divide by 100).
- Multiply: 0.18×250=450.18\times 250=450.18×250=45.
- So 18% of 250 is 45.
- Use the ‘over 100’ method
- Formula: percentage100×number\dfrac{\text{percentage}}{100}\times \text{number}100percentage×number.
- Example: 20% of 1200 = 20100×1200=0.2×1200=240\dfrac{20}{100}\times 1200=0.2\times 1200=24010020×1200=0.2×1200=240.
In words: “Take the percent, turn it into a fraction over 100 , then multiply by the number.”
Mini‑section 3: Quick mental tricks
People often use little shortcuts to make percentages easier in their head.
- 10% of a number: move the decimal one place left (10% of 250 is 25).
- 5% of a number: find 10% and then halve it (5% of 250 = half of 25 = 12.5).
- 1% of a number: divide by 100 (1% of 250 = 2.5).
- To find awkward percents like 18% of a number, you can do 10% + 5% + 3% (3% is 1% × 3), then add them up.
A neat trick from forum discussions: n%n%n% of mmm is the same as m%m%m% of nnn. For example, 4% of 25 is the same as 25% of 4 (which is 1).
Mini‑section 4: Three common “percentage of a number” problem types
Most real‑life questions fall into one of these patterns.
| Problem type | Question shape | Formula | Example |
|---|---|---|---|
| Find percent | What percent is part of whole? | $$(\text{part} ÷ \text{whole}) × 100$$ | 26 out of 50 students → $$(26 ÷ 50) × 100 = 52\%$$ | [1]
| Find part | What is P% of number? | $$(P ÷ 100) × \text{number}$$ | 18% of 250 → $$(18 ÷ 100) × 250 = 45$$ | [5][9]
| Find whole | P% of what number is part? | $$\text{whole} = \dfrac{\text{part}}{P ÷ 100}$$ | 45 is 18% of what? → $$45 ÷ 0.18 = 250$$ | [9]
Mini‑section 5: A tiny story to remember it
Imagine you have a box of 100 identical tickets. Every percentage question is really asking: “If I had the same situation but with exactly 100 tickets, how many of them would be the ones I care about?”
- When you compute partwhole×100\dfrac{\text{part}}{\text{whole}}\times 100wholepart×100, you’re saying: “If I reshaped this group into 100 tickets, how many would be marked?”
- When you do percent100×number\dfrac{\text{percent}}{100}\times \text{number}100percent×number, you’re starting from “I know how many tickets out of 100 I want, now scale that up to my real number.”
If you tell me a specific example like “find 15% of 260” or “what percent is 30 of 80,” I can walk through the exact steps with you.
