Three Less Than a Number

Date: 08/19/2001 at 20:34:23
From: brian clarke
Subject: Algebra expressions

Why is this expression driving me crazy when at first it seems so 
simple?

 three less than a number

I believe it is x-3 but I am being challenged that it is 3-x.

Date: 08/20/2001 at 08:36:58
From: Doctor Peterson
Subject: Re: Algebra expressions

Hi, Brian.

You're right: you start with the number x and decrease it by 3, so 
that the new number is 3 less than what you started with.

Many people get confused by this sort of expression, because they 
expect to translate directly from English to Mathish, word for word. 
Then "three (3) less than (-) a number (x)" would seem to be "3-x". 
But it isn't. What's even more confusing is that "3 less a number" 
_does_ mean "3-x" because "less" as a preposition means the same as 
"minus."

If they had enough experience translating languages, they would 
understand that you have to translate idea for idea. I recommend first 
picturing what is happening (translating English to an idea, that of 
decreasing a number) and then putting that into an expression.

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