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How to Subtract Percentages (of the Same Whole Number) (Mathematics Lesson)

How to Subtract Percentages (of the Same Whole Number)

Percentages subtract in the same way as normal numbers.

As percentages are a way of expressing part of a whole number, the percentages must refer to the same whole number if you are to subtract them.

A Real Example of Subtracting Percentages

Question: What is 45% of a number subtract 15% of the same number?

45 - 15 = 30.

45% subtract 15% is 30%.

Visualizing Subtracting Percentages

A percentage shows how many parts out of a hundred. The grid below is made up of a hundred squares:

The grid below has 45 squares (representing 45%) in blue.

From these 45 squares, subtract the 15 squares (representing 15%) in red.

There are 30 remaining blue squares (representing 30%).

This lets us see that 45% subtract 15% is 30%.

The slider below gives another example of subtracting percentages.
Interactive Test

Don't Get Confused with Percentage Changes

Imagine a rise in interest rates from 10% to 15%. How would you describe this rise?

There are 2 ways of looking at this. The first is the way described on this page:

  • Subtract 10% from 15%. This gives a rise of 5 percentage points.
The other way is to describe it as a percentage change. Percentage changes are given by the formula below:

where nold is the old value and nnew is the new value.

In this case, nold is 10% and nnew is 15%.

Putting this in the above formula gives the percentage change as:

So, the second way of describing the rise is:

  • The percentage change from 10% to 15% is a 50% rise
Don't confuse the 2 ways!

Percentage Points and Percentages

A percentage point is 1%. They are useful when talking about absolute changes or differences in percentages.

The per cent sign "%" (or percentage) refers to relative changes or differences.

Basis Points

A basis point is one hundredth of 1%.

In other words:

100 basis points = 1%

Basis points are often used in finance, where there are small changes in percentages.