# 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.
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# 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.