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### Writing Ratios

```
Date: 06/03/99 at 21:09:28
From: Gary Grazioli
Subject: Ratios and Rates

Write a ratio in three ways. 11 out of 32 students have blue eyes. One
way is 11/32.

Can you help?
```

```
Date: 06/04/99 at 08:40:41
From: Doctor Rick
Subject: Re: Ratios and Rates

Hi, Gary.

I can think of two other ways to write this. One is the classic way of
writing ratios, using a colon. For instance: The ratio of blue-eyed
students to all students is 11:32. Read this as "11 to 32."

The other way I have in mind doesn't have the numbers 11 and 32, but
it has the same meaning. A percentage is a form of ratio: 10% means
"10 out of 100." We can follow the rules for writing an equivalent
fraction and make the denominator 100. The numerator won't necessarily
be a whole number, so what we get isn't what we normally think of as a
fraction, but it is a ratio.

11/32 = ?/100

What do we multiply 32 by to get 100? The answer is 100/32 = 3.125. If
we multiply numerator and denominator by 3.125, we get

11 * 3.125   34.375
---------- = ------ = 34.375%
32 * 3.125     100

In other words, 11 out of 32 is the same ratio as 34.375 out of 100.

Here is some further help on ratios from our Archives:

What is a ratio?
http://mathforum.org/library/drmath/view/58018.html

Figuring Ratios
http://mathforum.org/library/drmath/view/58012.html

Ratios
http://mathforum.org/library/drmath/view/58027.html

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions
Middle School Ratio and Proportion

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