Math Tutor – Online and In Home – Understanding Percentages

For many, percentages are confusing. Sometimes people don’t speak when they say things like ‘I gave 110% effort’ when of course you can’t give more than 100% by definion.

First lets look at how to read it: 50% is read as “Fifty per cent”.

The ‘per cent’ bit means ‘parts of a hundred’ so think of 50% as being fifty parts of a hundred – in other words, it is exactly half of something. So 50% of 20 is half of 20, or 10.

So how do we do simple percentage sums, then? Let’s look at one:

Calculate 40% of 50.

It’s always a good idea to turn maths which is abstract into a real life example. So we can think of this as saying “what is forty percent of 50 oranges”?

Now, imagine the old game where you say “one for me, one for you” and dividing those oranges up. But this time, for every 4 oranges for me, we feel generous and give you 6. This means that for every ten oranges we have, you get 6 and I get 4. To get from ten oranges to fifty oranges, you multiply by five, so I end up with 4 x 5 oranges which is of course 20 oranges. So that’s the answer.

If you read and followed the above paragraph, your key question will probably be “but how do I get from knowing that for every 10 oranges, I keep 4?”

Great question! And understanding that is the heart to doing percentage sums. Remember that the ‘%’ sign means ‘per hundred’ and so 40% means ’40 from every 100′. And our specific sum asks us to calculate this from 50 oranges. So what we need to do is work out the relation between 100 and 50. If we take 40 oranges for every 100, then how many oranges do we take from 50?

All we need to do is divide 50 by 100, to get 1/2. We then multiply this by 40 to find how many I get from 50, and find the answer is 20.

Do you Understand how this works?

This is really important to get your head round, but can be hard. Read through the above until you understand what a percentage means and what the method to solve the question is and why it works. Understanding percentages and what they represent is the key to being able to solve percentage sums – just learning the method is not the best way of solving them though it gives you the answer.

Here’s one final representation of this sum for you:

– If I have 100 oranges, and I take 40 of 100, how many do I have? Answer: 40 oranges!
– If I have 50 oranges, and I take 40 of 100, how many do I have? Answer: 20 oranges!

Final recap: to calculate a percentage like this, simply divide the number of items we have by 100, and multiply by the percentage. So, 40% of 50 becomes this sum: (50 / 100) x 40. This equals 1/2 x 40 which is 20.


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Stuart Raffeld

B. A. Operations Research & Statistics, California State University, Long Beach, Teaching Assistant undergraduate Mathematics. B.S. Mathematics, California State University, Long Beach. Mathematics University of California, Irvine, Teaching Assistant undergraduate Mathematics. Completed course work for MS Degree with 4.0 GPA. M.S. Mathematics, Kingsbridge University. Transcript available upon request. 1988-Present: Mathematics tutoring--One on one tutoring for SES students through YP institute and Academic advantage. Tutored students with low learning skills as well as very bright students. Tutored groups of four students in math classes from basic mathematics through calculus. Mathematics teaching for EFN, Inc., a private school.

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