Complementary Percentages

Poisonous Red Back Spider
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In Australia there are between 50 and 100 venomous species of Spider, but only two of these are life threatening to humans: the red-back and the Sydney funnelweb spider.

Based on this we could say that 3% of Ausralian Spiders are life threatenting to humans.

This means that 97% of Australian spiders are not life threatening.

The 97% figure was worked out by doing 100 – 3 = 97.

This is called using “Complementary Percentages”, and is the subject of this short lesson.


Complementary Percentages

Complementary Percentages add up to 100%, where 100% refers to the Grand Total amount.

30% and 70% are complementary percentages: (30 + 70 = 100) .

40% and 60% are complementary percentages: (40 + 60 = 100) .

20% and 80% are complementary percentagess: (80 + 20 = 100) .

Complementary Percentages are useful for finding out a missing percentage, if we know the other percentage.

For example if 70% of people like chocolate ice cream,
then 100 – 70 = 30% of people do not like chocolate ice cream.

If 60% of the students in a class are girls,
then we can work out that 100 – 60 = 40% of the class are boys.

If 43% of the population in India live in Urban areas,
then 100 – 43 = 57% of the population live outside of Urban areas.

The two percentages always have to add to 100.

So to find the missing percent, we do 100 – the percentage we know.

This can be a useful thing to remember when working out mathematics questions.


Complementary Percentages Examples

Crowd making USA flag at football game
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According to Wikipedia, the United States of America is home to 4.52% of the earth’s population with more than 307,000,000 people. (as of July 17, 2010)

What percentage of the world’s population lives outside of the USA ?

We can use Complementary Percentages to work this out, because people either live in the USA or not in the USA.

Percentage of People not living in the USA = 100 – 4.52 = 95.48%.


Girl with Driving Instructor in car
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If 80% of a group of 40 students passed their driving license test on the first attempt, then how many students failed the test ?

We know that 80% passed, so 100 – 80 = 20% did not pass because they failed.

20% of 40 = 20 divided by 100 x 40

= 8 students failed their driving test.


NASA picture of planet earth's atmosphere
Image Source:

The idea of percentages adding to 100 in total, is not just limited to having two items.

Air in the earth’s atmosphere typically contains 78% nitrogen, 20% oxygen, 1% water vapour, 0.93% argon and 0.04% carbon dioxide.

The rest is made up of other gases.

What is the percent of other gases?

We can work this out by doing :

100 – 78 – 20 – 1 – 0.93 – 0.04

= 0.03% other gases.


Related Items

Introduction to Percentages
Converting Percentages to Fractions
Converting Percentages to Decimals
Converting Fractions to Percentages
Converting Decimals to Percentages
Converting Percentages (All Types)
Interesting Percentages
Percentages and Weight Training
Decimals and Percentages Games


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