# Percentages

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

## Calculating a score as a percentage

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  ## Calculating percentages – using fractions

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

Example

Find 20% of £45 ## Calculating percentages – using decimals

Convert to a decimal, then multiply.

Example

Find 20% of £45 ## Calculating percentages –  using units

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

The required  percentage can then be built up.

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  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

## Calculating percentages –  using the calculator

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