MATHEMATICSNumber & Arithmetic

CURRENT TOPICPercentages

NAVIGATION

● Not StartedIntermediate 30 minTopic 6 of 8

Percentages

Percentages appear across 11+ papers in data, fractions, and real-world money problems. Master conversions, finding proportions, and applying percentage changes flawlessly.

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What you'll learn

4 core skill areas across this topic

Percentage of Amount

Calculate fundamental percentages (10%, 5%, 1%) and combine them for any value

Percentage Change

Find the new value after a percentage increase (e.g. tax, interest) or decrease (e.g. sale, discount)

FDP Conversions

Fluidly convert between Fractions, Decimals, and Percentages to solve mixed problems efficiently

Reverse Percentages

Work backwards from a post-increase/decrease value to find the original 100% amount

Essential Equivalents

Memorise these FDP (Fraction-Decimal-Percentage) conversions to speed up calculations.

50%

1/2 = 0.5

25%

1/4 = 0.25

10%

1/10 = 0.1

75%

3/4 = 0.75

20%

1/5 = 0.2

1/100 = 0.01

Mental Math Building Blocks

Break down tricky percentages into easy combinations of 10%, 5%, and 1%.

÷10

Finding 10%

Move the digits one place value to the right (divide by 10).

Example

10% of 340 = 34

÷100

Finding 1%

Move the digits two place values to the right (divide by 100).

Example

1% of 340 = 3.4

Finding 5%

Find 10% first, then halve your answer.

Example

5% of 340 = 17

Combine the blocks to find any amount!

E.g., to find 16% of 340, you can calculate:
10% (34) + 5% (17) + 1% (3.4) = 54.4

Percentage Change & Reverse Percentages

Real-world applications tested frequently at 11+

📈

Percentage Increase

Tip: Find the percentage amount, then ADD it to the original. Or use the multiplier method.

Increase £80 by 15%

10% of 80 = 8
5% of 80 = 4
15% = 12
New total: 80 + 12 = £92

📉

Percentage Decrease

Tip: Find the percentage amount, then SUBTRACT it from the original.

Decrease £60 by 20%

10% of 60 = 6
20% of 60 = 12

New total: 60 - 12 = £48

Key facts to remember

💡

Percent literally means "out of 100". 45% is 45 out of 100.

🔄

Percentages are reversible! 8% of 25 is exactly the same as 25% of 8.

➕

To increase by 15%, you can just multiply by 1.15.

➖

To decrease by 20%, you can just multiply by 0.80.

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