Solving an Equation with Decimals

Date: 1/31/96 at 19:57:19
From: Anonymous
Subject: Algebric Equations

I can't figure out what 15.6 + z = 20.4 is.  
I need step by step help.

Date: 2/2/96 at 10:40:11
From: Doctor Elise
Subject: Re: Algebric Equations

The way you solve any algebra problem is by putting all the 
letters on one side of the equals sign, and all the numbers on the 
other.  The rule is that you can do anything you want to the 
equation as long as you do the same thing on both sides of the 
equals sign.

Okay.

15.6 + z = 20.4

What we need to do is get the equation to look like "z = 
something".

So we need to subtract the 15.6 from the left side of the equals 
sign.
We have to do the same thing to both sides, so what we'll do is 
this:

15.6 + z - 15.6 = 20.4 - 15.6

From the very beginning of math, you learn that 2 + 3 = 3 + 2, our 
old friend the "commutative property" of addition.  What this 
really means is that if you have to add and subtract numbers (and 
letters) you can rearrange them in any order and it doesn't make 
any difference.  In fact, rearranging the order is about the ONLY 
thing you don't have to do to both sides of the equals sign.  So I 
can write:

15.6 - 15.6 + z = 20.4 - 15.6

Now, 15.6 - 15.6 is 0, so now I have:

0 + z = 20.4 - 15.6

I know that 0 + z is equal to z, so I'll get rid of the 0 and get

z = 20.4 - 15.6

And then you can go ahead and do the 20.4 - 15.6 part.  Be sure to
estimate first so that you know what your answer should be: after 
all, this is "a little more than 20 minus a little more than 15", 
so the answer should be pretty close to 5.

Good luck!

-Doctor Elise,  The Math Forum