Finding a Percentage of an Amount

What "percent of an amount" means

Percentages are everywhere: a 20% discount in a shop, 15% interest, 60% in a test, a 5% tip. Finding a percentage of an amount lets you answer the practical question "how much is that?" In this lesson you will learn three reliable methods — the 10% and 1% building blocks, fraction shortcuts, and the decimal multiplier — and when to use each.

First, the key idea: percent means "out of 100". So 25% is 25 out of 100, which equals the fraction 25/100 and the decimal 0.25. For a fuller introduction to what percentages are, see our Percentages Made Easy lesson. Remember too that "of" means multiply, so "25% of 80" means 25/100 × 80.

Method 1: the 10% and 1% building blocks

This is the best method for working in your head or without a calculator. You find two easy "building blocks" and combine them.

10% of a number = divide by 10. 1% of a number = divide by 100.

From these you can build any percentage by adding, doubling or halving.

Example 1 — Find 10% of 80.

1. Divide by 10: 80 ÷ 10 = 8.
2. So 10% of 80 = 8.

Example 2 — Find 30% of 50.

1. Find 10% first: 50 ÷ 10 = 5.
2. 30% is three lots of 10%: 5 × 3 = 15.
3. So 30% of 50 = 15.

Example 3 — Find 15% of 200.

1. 10% of 200 = 200 ÷ 10 = 20.
2. 5% is half of 10%: 20 ÷ 2 = 10.
3. Add them: 15% = 10% + 5% = 20 + 10 = 30.

Example 4 — Find 17% of 300 using 1%.

1. 10% of 300 = 30.
2. 1% of 300 = 300 ÷ 100 = 3, so 7% = 3 × 7 = 21.
3. Add: 17% = 10% + 7% = 30 + 21 = 51.

Method 2: fraction shortcuts

Some percentages are well-known fractions, which makes them very quick.

Percentage	Fraction	What to do
50%	1/2	divide by 2
25%	1/4	divide by 4
75%	3/4	divide by 4, then × 3
20%	1/5	divide by 5
10%	1/10	divide by 10

Example 5 — Find 25% of 60.

1. 25% is a quarter, so divide by 4: 60 ÷ 4 = 15.
2. So 25% of 60 = 15.

Example 6 — Find 75% of 40.

1. 75% is three quarters. First find one quarter: 40 ÷ 4 = 10.
2. Multiply by 3: 10 × 3 = 30.
3. So 75% of 40 = 30.

Method 3: the decimal multiplier

This is the fastest method on a calculator. Write the percentage as a decimal, then multiply.

Rule: percentage of an amount = (percentage ÷ 100) × amount. Dividing by 100 turns the percentage into a decimal multiplier.

So 30% becomes 0.30, 7% becomes 0.07, and 45% becomes 0.45.

Example 7 — Find 30% of 50.

1. Write 30% as a decimal: 30 ÷ 100 = 0.3.
2. Multiply: 0.3 × 50 = 15.

Example 8 — Find 8% of 250.

1. 8% as a decimal: 8 ÷ 100 = 0.08.
2. Multiply: 0.08 × 250 = 20.

All three methods agree — choose whichever suits the numbers and whether you have a calculator.

A reference table

Find	Easiest method	Working	Answer
10% of 90	divide by 10	90 ÷ 10	9
50% of 46	divide by 2	46 ÷ 2	23
25% of 80	divide by 4	80 ÷ 4	20
20% of 35	divide by 5	35 ÷ 5	7
35% of 200	10% + 10% + 10% + 5%	20+20+20+10	70
12% of 150	decimal multiplier	0.12 × 150	18

Why the building blocks work

The 10% and 1% method feels almost too easy, so it helps to understand the why. Percent means "out of 100", so 10% = 10/100, which simplifies to 1/10. Taking one tenth of a number is exactly the same as dividing by 10 — that is why 10% of 80 is 80 ÷ 10 = 8. In the same way, 1% = 1/100 = 1/100, so finding 1% means dividing by 100.

Once you have these two building blocks, every other percentage is just a combination. 30% is three tens of percent, 5% is half of 10%, and 1% lets you reach any odd value like 7% or 23%. Because percentages add up neatly (15% really is 10% plus 5%), you can construct any percentage you need from pieces you can work out in your head. The decimal multiplier is the same idea in compact form: dividing the percentage by 100 is what turns "out of 100" into a number you can multiply by.

A worked real-life example

A jacket costs £60 and is reduced by 25% in a sale. How much do you save, and what is the new price?

1. Find the saving: 25% of £60. Using the fraction shortcut, 60 ÷ 4 = £15 saved.
2. Find the new price: £60 − £15 = £45.

You could also find the new price directly: paying 75% of the original is 0.75 × 60 = £45. Both routes agree.

A practice activity

Use a shopping flyer, a menu, or just made-up prices.

1. Pick an item priced at a round number, say £40.
2. Work out 10% of it by dividing by 10 (£4). Then find 20% (double it: £8) and 5% (halve the 10%: £2).
3. Imagine a 15% discount. Add 10% + 5% = £4 + £2 = £6 off, giving a new price of £34.
4. Check with the decimal method: 0.15 × 40 = £6. They match.

Then try these on paper (answers below): (a) 10% of 70, (b) 50% of 18, (c) 25% of 48, (d) 30% of 90, (e) 5% of 200.

Answers: (a) 7, (b) 9, (c) 12, (d) 27, (e) 10.

Where this leads

Finding a percentage of an amount is the basis for discounts, interest, tax, tips and percentage change. It links directly to fractions and decimals, since a percentage is simply a fraction out of 100 written as a decimal. To strengthen those connections, revisit Percentages Made Easy. The fastest habit to build is the 10% and 1% method — with those two blocks you can find almost any percentage in your head.