Percentages Without a Calculator

Percentages are everywhere: discounts, tips, VAT, exam grades, phone battery, interest rates. If you can find 10 percent and 1 percent in your head, you can build almost any percentage you will meet in daily life, and feel far more in control of your money.

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Watch the full video guide for this module

First, a word for anyone who feels 'bad at maths'

• The UK Department for Education's Education Hub, writing for National Numeracy Day 2025, says there is no 'maths gene': numeracy ability comes from nurture, not nature, and most people can improve and overcome maths anxiety.
• The same article points out that real-world maths is different from school maths, and that feeling anxious, stressed or exposed when faced with numbers is common.
• Everyday maths is mostly a handful of tricks used again and again. This module teaches those tricks with worked examples you can copy.
• Practise out loud or on paper. Showing your steps, rather than jumping to an answer, is what builds confidence.

The building blocks: 10, 5 and 1 percent

• To find 10 percent, divide by 10: move the decimal point one place to the left. Third Space Learning gives the example 10 percent of 60 = 6.
• To find 5 percent, halve the 10 percent figure. To find 1 percent, divide by 100 (or divide your 10 percent figure by 10 again).
• Worked example on AED 240: 10 percent is 24, 5 percent is 12, 1 percent is 2.40.
• Now build: 15 percent = 10 percent + 5 percent = 24 + 12 = AED 36. 20 percent = 2 x 24 = AED 48. 50 percent is simply half, AED 120. 25 percent is half of that, AED 60.
• Another build: 35 percent of 80 = three lots of 10 percent (3 x 8 = 24) plus 5 percent (4) = 28.
• A handy trick: percentages are reversible. 8 percent of 25 is the same as 25 percent of 8, which is 2. Swap the numbers if one way round is easier.

Increases and decreases with multipliers

• Tutorful explains the multiplier method: to increase by p percent, multiply by 1 + p/100; to decrease by p percent, multiply by 1 minus p/100.
• Increase example from Tutorful: an 80 pound football shirt rising by 15 percent costs 80 x 1.15 = 92 pounds.
• Decrease example from Tutorful: a 450 pound laptop with 20 percent off costs 450 x 0.80 = 360 pounds.
• Multipliers can be chained. A price that goes up 20 percent and then down 20 percent does not return to where it started: 100 x 1.2 x 0.8 = 96.
• Reverse percentages: if trainers cost 63 pounds after a 30 percent reduction, the original price was 63 divided by 0.70 = 90 pounds (Tutorful). Do not add 30 percent of 63 back on; that gives the wrong answer.

Percentage change: always divide by the starting value

• Tutorful's rule: percentage change = change divided by the original value, multiplied by 100.
• A price rising from AED 40 to AED 50 is a rise of 10 on a start of 40: 10 / 40 = 25 percent.
• The same AED 10 change going down, from 50 to 40, is 10 / 50 = 20 percent. The starting point changes the answer.
• This is why 'up 25 percent then down 20 percent' can bring you back to exactly the same price.

Percent versus percentage points

• Mathwords defines a percentage point as the simple difference between two percentages, without dividing by the original value.
• Mathwords' example: a sales tax rising from 6 percent to 9 percent has risen by 3 percentage points, but by 50 percent relative to the original rate, because 3 is half of 6.
• Both statements are true, but they sound very different. Headlines, banks and politicians sometimes choose whichever sounds bigger or smaller.
• When you see a change in a rate (interest, tax, exam pass rate, unemployment), ask: is this percentage points or percent?