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

### Is Full Equal to Empty?

```
Date: 06/15/99 at 13:03:06
From: Joseph
Subject: A weird question

Hi, Joseph again! I have a question I could not understand. Could you
help me? thanks!

1/2 full = 1/2 empty

So when we multiply both sides of the equation by 1/2, won't we get
full = empty?
```

```
Date: 06/15/99 at 17:39:53
From: Doctor Rick
Subject: Re: A weird question

Hi, Joseph.

Cute! This is just one of many examples of why we don't use English as
the language of mathematics. "Half empty" does not mean "1/2 times
empty."

If we let full mean V (volume of a full glass) and empty mean 0
(nothing in the glass), then you would have

1/2 * V = 1/2 * 0

which is, of course, false (unless the glass can't hold anything -
then V = 0).

What we really mean by "half empty" is halfway from full to empty,
while "half full" means halfway from empty to full. If I were to
translate the phrases into math, they would be

half full:  0 + 1/2 * V
half empty: V - 1/2 * V

These, of course, are equal.

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

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