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Order of Algebraic Operations

Date: 25 May 1995 18:22:51 -0400
From: Richard Seguin
Subject: Algebraic Operations

I seem to have a problem with these types of questions. I don't really know
how to take them apart and solve them.

Here are two I would like you to help me with please.

        1)     9*4-7*5+6*7-10
               ----------------  =  ?

        2)    2+2*3-(2/2)*(4-3)+1 = ?

I can't figure out where I cut it in half.


Date: 26 May 1995 19:07:11 -0400
From: Dr. Ken
Subject: Algebraic Operations

>        1)     9*4-7*5+6*7-10
>               ----------------  
>               6/6+7*3-4*3-9 

Okay!  The first thing you should realize about this problem is that no
matter what you do, you should evaluate the top of the big fraction and the
bottom of the big fraction separately, and then divide the two answers you
get.  So really what you should do is simplify the top, simplify the bottom,
and then do the division.  Sound good?

When we simplify the top, (the top is 9*4-7*5+6*7-10) we have to remember
the order of operations.  We do all the * and / before we do any + and -.
So if we go through and take care of all the * and / in the top, we get 
36 - 35 + 42 - 10 in the top.  Right?  Can you simplify this?  

Now you've got to do the same thing with the bottom (the bottom is 
6/6+7*3-4*3-9).  Do the * and / first, and then just go through and do the
addition and subtraction.  Then you'll just have a number in the top, a
number in the bottom, and you'll divide them.

>        2)    2+2*3-(2/2)*(4-3)+1 

In this problem, look at the parentheses ().  Whenever you see parentheses,
you can do whatever math is inside them first, and then once that's done you
can take another look at the problem.  So if we do the math that's inside
those parentheses, we get 2+2*3-1*1+1.  Now we do the same thing we did
above, do all the * and / first, and then all the + and -.  

If you want to check your answers, or you need more help on the problems,
let us know!

-Ken "Dr." Math
Associated Topics:
Middle School Algebra

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