Associated Topics || Dr. Math Home || Search Dr. Math

### Estimating Fractions

```
Date: 12/02/2001 at 17:36:41
From: Justin
Subject: Estimating Fractions

Dr. Math,

I am completely clueless about the process of estimating fractions.
Here is a simple example of an estimation question using fractions:
There is a plate of assorted cookies. 1/6 of these cookies are
chocolate chip, while 1/5 of them are peanut butter. The rest of the
cookies on the plate are regular. What fraction do the regular

Sincerely,
Justin
```

```
Date: 12/03/2001 at 15:31:50
From: Doctor Ian
Subject: Re: Estimating Fractions

Hi Justin,

In this case, I think what you're supposed to recognize is that 1/5
and 1/6 are very close to the same fraction, with 1/5 being a little
larger.

So one way you might proceed would be to say that

1/5 + 1/6 ~ 1/5 + 1/5 = 2/5

which would leave 3/5 of the cookies as regular. (The '~' is
pronounced 'approximately equals'. It's this kind of approximation
that you're doing when you estimate something.)

On the other hand, you might say that

1/5 + 1/6 ~ 1/6 + 1/6 = 2/6 = 1/3

which would leave 2/3 of the cookies as regular. So you could say that
'between 1/3 and 2/5 of the cookies are regular'.

The idea is that this is much easier (and often much neater) than

1/5 + 1/6 = 6/30 + 5/30

= 11/30

Yuck!  Note that

1/3 = 0.3333...

11/30 = 0.3666...

2/5 = 0.40

so the real answer is in between the two estimates... which is exactly
what you'd expect if you made one estimate too large and the other too
small.

The basic idea with estimation is always the same: you agree to accept
a little less accuracy in exchange for doing a lot less work.
Sometimes that's a good trade, and sometimes it's not. Part of
learning to estimate things is learning when estimation is a good
idea, and when it's a bad idea.

I hope this helps.  Write back if you'd like to talk more

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions
Middle School Fractions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search