Percentages as Comparisons

Date: 11/18/98 at 21:41:30
From: Dyana Goldman
Subject: How do you find what percent 45 is of 82?

How do you find what percent 45 is of 82?

I looked at your site and saw that someone had asked the same question, 
except they asked what percent 27 is of 76. I did not at all understand 
the explanation. Could you help me?

Date: 12/22/98 at 11:27:30
From: Doctor Matthew
Subject: Re: How do you find what percent 45 is of 82?

That's a good question!

What exactly is a percentage? You can think of it as the concept of 
"how big one thing is compared to another." This sounds funny, but it's 
what a percentage is. So if item A is 100% of item B, then items A and 
B are the same "size." (Remember that percentages are in units of 100, 
so anything less than 100 is smaller, and anything more than 100 is 
larger).

When we say (for example) that a number is 50% of another number, we 
know that the first number is half the second.

Let's deal with a more complicated example.

Pretend that you have 4 of your friends with you, 3 of them have brown 
hair, and 1 of them has red hair. You want to know what percentage of 
your friends has red hair. (Here's part of your answer: it's almost 
always easier to find out the fraction part first, and then do the 
percentage). You have a total of 4 friends, and only 1 with red hair, 
so the percentage is 1/4 (percentage-fractions work like this, you put 
the number of the thing you want to find on the top, and the total 
number on the bottom). 

To find the percentage, you do the following, long divide the fraction 
that you find (in our case 1/4, which works out to be .25), then 
multiply it by 100, and that's your percentage (25%). Now to find the 
fraction that the percentage is, it's also very simple. The numerator 
of the fraction (remember that's the top part) is the number of the 
percentage (25) and the denominator is 100. So the fraction is 25/100, 
which we know we can reduce to 1/4. So there's your answer!

I hope this helps!

- Doctor Matthew, The Math Forum
  http://mathforum.org/dr.math/