# Complementary Percentages

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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

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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%.

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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.

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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.

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Enjoy,
Passy

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