How to Interpret "Increase" in Word Problems

Date: 10/19/2004 at 07:02:43
From: Sonia
Subject: What is 3.7 increased by 1/10

I have tried the question to increase 3.7 by 1/10, but my answer has
not increased, it's decreased from 3.7 to 0.37.  I got this by doing
3.7 x 1/10.  Please explain this to me.

Date: 10/19/2004 at 09:41:36
From: Doctor Peterson
Subject: Re: What is 3.7 increased by 1/10

Hi, Sonia.

The phrase you are answering is one that is very easy to confuse with 
similar phrases.

If I say "multiply 3.7 by 1/10", I mean 3.7 * 1/10 = 0.37.  Note that 
we don't use the word "increase" to talk about multiplication, even 
though multiplying by a number greater than 1 does increase a number.  
The word is reserved for addition, as in the next case.

If I say "increase 3.7 by 0.1", I probably mean 3.7 + 0.1 = 3.8.  To 
increase a number is to add something (positive) to it.

If I say "increase 3.7 by 1/10" (or, more often, "by 10%"), I mean 
to add a tenth OF 3.7 TO 3.7.  That is, 1/10 of 3.7 is 0.37, and I 
want to increase 3.7 by that amount: 3.7 + 0.37 = 4.07.

The last of these is what you were asked for.

If you have any further questions, feel free to write back.


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