Translating English to Algebra

Date: 06/27/2002 at 22:38:06
From: Nicole Weaver
Subject: algebraic expression

Write an algebraic expression for 

  Seven more than twice a number.

The problem I am having is to determine how to differentiate between 
more than/less than as in inequalities, or plus and minus.

Date: 06/28/2002 at 12:55:35
From: Doctor Peterson
Subject: Re: algebraic expression

Hi, Nicole.

The difference is that "greater than" and "less than" in inequalities 
are really verbs: "7 > 2N" means "seven IS MORE THAN twice a number". 
What you are given is not a complete sentence like that (with a 
verb), but just a phrase. Phrases correspond to expressions in math. 
In fact, if you are told to write an expression, you will NEVER have 
to use ">" or "<", because they don't go in expressions!

If I said "My age is seven more than twice her age", I have used a 
phrase equivalent to the one you are given. How would I interpret it? 
If I knew her age (say, 14), I could find my age by doubling her age 
(to 28) and then adding 7 (making 35). I added 7 because I know that 
my age is not just "more than" her age, but "seven more than" her 
age, meaning that I have to add 7 to hers to get mine.

Now to write an expression for this, I just take a variable, say N, 
and do to it just what I did to the presumed age a moment ago. I 
start with N, then double it to get 2N ("twice a number"). Then I add 
7 to it to get 2N+7, which is seven more than 2N.

Taking it step by step this way, and thinking through how you would 
calculate a value if you knew the starting number, allows you to 
build the expression piece by piece.

Does that help?

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