Checking Your Work

Date: 9/9/96 at 22:1:45
From: Anonymous
Subject: Little (stupid) mistakes

Dr. Math,

I've had problems keeping myself from doing little mistakes such 
as not putting commas in, putting the decimal point in the wrong 
place, and writing down the wrong number (though I HAVE gotten better 
about that!).  I've tried to check over everything, but I still end up 
making those mistakes (I have to admit, I DO do better if I check over 
everything)!  How can I stop doing this?

Jennifer

Date: 9/10/96 at 19:56:40
From: Doctor Tom
Subject: Re: Little (stupid) mistakes

Hi Jennifer,

There are a few things you can do:

1)  Check your answer by plugging it back into the equations
    or into the problem to see if it works.

For example, if you're solving for x in: 5x - 3 = 17,
and you get x = 5, try it out:  5*5 - 3 = 17?  25-3 = 17? 22=17?
Nope!

2)  This method works better for word problems than equations,
    and that's to try to get a feeling for what the answer should
    be before you work it out (at least roughly).  Then see if the
    answer you get is out of the ballpark.  For example, suppose
    you're talking about a trip to the store, and you buy items
    costing $1.76, $2.43, $5.01, $11.43, ... about 10 items like
    that.  What's the total cost?  Take a look at all the numbers.
    In this case, it looks like the rough "average" (just by
    eye-balling them) is about 5 bucks each.  So an answer of
    about $50 is roughly right.  If you get $500 or $5, you know
    you're out of the ballpark.

3)  If you can figure out how to do a problem in more than
    one way, this is the best solution of all.  Your answers
    had better agree.  Even for simple problems like addition
    you can do this.  For example, when I'm adding up the
    numbers in my checkbook, if I really care about the answer,
    I'll do it twice, but once I'll start typing them into the
    calculator from the top of the list to the bottom, and the
    next time, I'll type them in from bottom to top.  If I do
    it the same way both times, I'm much more likely to make
    the same mistake both times.

I hope this helps some.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/