# How to Add Percentages (of the Same Whole Number)

Percentages add 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 add them (see the Beware at the side).

# A Real Example of Adding Percentages

Question: What is 20% of a number add 45% of the same number?

20 + 45 = 65.

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

The grid below has 20 squares (representing 20%) in blue and 45 squares (representing 45%) in red.

If the blue squares are added to the red squares (and they are all coloured purple), there are 65 coloured squares. This is 65%:

This lets us see that 20% add 45% is 65%.

The slider below gives another example of adding percentages.
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##### Note
DO I ALWAYS JUST ADD PERCENTAGES?

No!

Look at the following. Add the following squares:

Adding the two percentages gives 50 + 50 = 100%.

This is clearly not the case. There are 100 coloured squares, but there are now 200 squares over all. Only 50% of the squares are coloured.

This is why it is so important that to add percentages, each percentage must apply to the same whole.

50% of a grid add 50% of the same grid (the same whole) does equal 100% of the grid.

The key point is:

Only add percentages when the parts refer to the same whole!