# 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.

##### Interactive Test

**show**

##### 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!**