The word percent means “out of one hundred”

% means ÷ 100

Percentages are just fractions with a denominator of 100

Examples

As simplified fractions:

And as decimals:

Converting between percentages ,fractions and decimals

This is just the same as turning a fraction into a percentage.

Example

Fred attained 23 marks out of 40 for his test.

What was has score as a percentage ?

Sometimes it is easier just to calculate the equivalent fraction that gives a denominator of 100:

Examples

Convert the percentage into a fraction then follow the rules for calculating fractions.

Example

Find 20% of £45

Convert to a decimal, then multiply.

Example

Find 20% of £45

to find 1% of a value – just divide by 100

to find 10% of a value – just divide by 10

to find 100% of a value – just divide by 1

Example

Find 20% of £45

Useful tips:

- To find 0.1%, divide 1% by 10
- To find 2% , double 1%
- To find 3% , add 2% and 1%
- To find 4% , double 2%, or subtract 1% from 5%
- To find 6% , add 5% and 1%
- To find 7% , add 5% and 2%
- To find 8% , add 5% and 3% or subtract 2% from 10%
- To find 9% , add 5% and 4% or subtract 1% from 10%

To find 5% , half 10% or multiply 1% by 5

- To find 20% , double 10% or divide value by 5 (since 20%= 1/5)
- To find 25% , add 20% and 5% or divide value by 4 (since 25%= 1/4)
- To find 30% , multiply 10% by 3
- To find 33 1/3% , divide value by 3 (since 33 1/3% = 1/3)
- To find 40% , multiply 10% by 4 or divide value by 5 then multiply by 2 (since 40%= 2/5)
- To find 50% , divide value by 2 or multiply 10% by 5
- To find 60% , multiply 10% by 6 or add 50% and 10%
- To find 66 2/3% , divide value by 3 then multiply by 2 (since 33 1/3% = 2/3)
- To find70% , multiply 10% by 7 or add 50% and 20%
- To find 75% , Add 50% and 25% or divide value by 4 then multiply by 3 (since 75%= 3/4)
- To find 80% , multiply 10% by 8 or subtract 20%
- To find 90% , multiply 10% by 9 or subtract 10%

Examples

VAT is currently at 20%, but used to be at 17.5%

To calculate VAT at 20 %, divide the value by 10 and double !

Examples

Calculate the VAT at 20% on an item costing £450.

A lawnmower costs £450 ex VAT.

What is the price inclusive of VAT ?

Vat @ 17.5% is very easy to calculate:

17.5% = 10% + 5% + 2.5%

so,

- Divide by 10 to get 10%
- Half your answer to get 5%
- Half that answer to get 2.5%
- Add all three up !

Example

Calculate the VAT due at 17.5% on an article costing £360.

VAT due is £63

Save yourself effort – divide the number in front of the percentage sign by 100.

100% = 1

10 % = 0.1

1% = 0.01 0.1% = 0.001

Examples

90% of £34,567 = 0.9 x 34,567 = £31,110.30

235.6% of £34,567 = 2.356 x 34,567 = £81439.85