Order of Operations Problems - a General Strategy

Date: 10/23/2002 at 17:21:09
From: Kara
Subject: Multiples

My homework was really hard. Can you tell me the answer to this 
problem? 

Make an equation using 7, 26, 46, and 15 to equal 160.

I have worked it out several different times and still cannot figure 
it out. Here's another one: how can you get 18, 9, 24, and 20 to equal 
18? At first I thought they looked easy, but I was wrong. Please help 
me.

Date: 10/23/2002 at 18:02:58
From: Doctor Ian
Subject: Re: Multiples

Hi Kara,

For a question like this, the answer is unimportant. The purpose of 
the question is to get you to generate a lot of _wrong_ answers, since 
that will give you practice in doing arithmetical operations 
(addition, subtraction, multiplication, and division). If we told you 
the answer, it would be sort of like going to soccer practice in your 
place. What would be the point? 

In the second part, I can give you this hint: It's possible to use 
9, 24, and 20 to make 36; and 36 - 18 = 18.

That, by the way, is a general sort of strategy you can use.  Pick 
out one number, and the result, and think about how you could get to 
the result in one step using that number. For example, to get to 160 
from 15, you might do one of these:

  160 = 15 + 145 

      = 15 * 12

      = 175 - 15

      = 2400 / 15

So now you have a set of smaller problems:  Can you use the other 
three numbers to make 145, 12, 175, or 2400?  If not, you can try 
again using one of the other numbers as your choice. 

Does this help? 

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