Finding a percent of a number

A common type of question:

What is 30 % of 80?

It's asking: out of 80, what's the size of the "30-out-of-100" share? The trick is to break the percent into friendly pieces you can do in your head.

The "1 % trick"

The cleanest method: find 1 % of the number first, then multiply by the percent you want.

1 % of 80 = 80 ÷ 100 = 0.8.
30 % of 80 = 30 × 0.8 = 24.

That works for any percent of any number — but it can get messy. For the friendly percents below, there are shortcuts that are much faster.

Percent	Trick
10 %	Divide by 10
20 %	Divide by 5 (or: 10 % + 10 %)
25 %	Divide by 4 (= halve twice)
50 %	Halve
75 %	Three quarters: halve and halve again, then add the two
1 %	Divide by 100

Once you know "1 % of X" and "10 % of X", you can build almost any percent:

Find 35 % of 60.
10 % of 60 = 6.
30 % of 60 = 3 × 6 = 18.
5 % of 60 = half of 10 % = 3.
35 % of 60 = 18 + 3 = 21.

Find 25 % of 64.
25 % = ¼, so 64 ÷ 4 = 16.

Find 75 % of 200.
75 % = ¾. Half of 200 is 100. Half of 100 is 50. 100 + 50 = 150.

Find 10 % of 240.
Divide by 10: 240 ÷ 10 = 24.

Find 20 % of 45.
10 % of 45 = 4.5. 20 % = double that = 9.

A jumper costs £40 and there's a 25 % discount. How much do you save?

25 % of 40 = ¼ of 40 = £10 off. The new price is 40 − 10 = £30.

A bus has 30 seats and 60 % are full. How many people are sitting?

10 % of 30 = 3. 60 % = 6 × 3 = 18 people.

Subtracting the percent from the number. "30 % of 80 is 80 − 30 = 50." No — that mixes up subtracting a percent from the whole with finding a percent of the whole. Always think "of" means multiply (× the percent ÷ 100).
Forgetting to convert. "30 % of 80 = 30 × 80 = 2400." That treats 30 % as the number 30. A percent must always be turned into either a decimal (× 0.30) or a friendly fraction (× 3/10) first.
Computing 25 % as a third instead of a quarter. 25 % is a quarter (1/4), because 25/100 = 1/4. A third is 33⅓ %.

A book has 200 pages. After reading 60 % of it, how many pages are left?

Same answer using the other side: 100 % − 60 % = 40 % left. 40 % of 200 = 4 × 20 = 80.