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

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.

20% add 45% is 65%.

Visualizing Adding 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 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.
Quick Test
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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!