Associated Topics || Dr. Math Home || Search Dr. Math

### 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

```
Associated Topics:
Middle School Equations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search