Beginning Algebra
Tutorial 6: Subtracting Real Numbers
Learning Objectives
After completing this tutorial, you should be able to:
 Subtract real numbers that have the same sign.
 Subtract real numbers that have different signs.
 Simplify an expression that has subtraction in it using the order of
operations.

Introduction
This tutorial reviews subtracting real numbers and
intertwines that
with some order of operation and evaluation problems.
I have the utmost confidence that you are familiar with
subtraction,
but sometimes the rules for negative numbers (yuck!) get a little mixed
up from time to time. So, it is good to go over them to make sure
you have them down.
Even in this day and age of calculators, it is very
important to know
these basic rules of operations on real numbers. Even if you are
using a calculator, you are the one that is putting the information
into
it, so you need to know things like when you are subtracting versus
adding
and the order that you need to put it in. Also, if you are using
a calculator you should have a rough idea as to what the answer should
be. You never know, you may hit a wrong key and get a wrong answer (it
happens to the best of us). Also, your batteries in your
calculator
may run out and you may have to do a problem by hand
(scary!!!).
You want to be prepared for those Murphy's Law moments.

Tutorial
Subtracting Real Numbers
a  b = a + (b)
or
a  (b) = a + b

In other words, to subtract b,
you add
the opposite of b.
Now, you do not have to write it out like this if you
are already comfortable
with it. This just gives you the thought behind it. 
Example
1: Subtract 3  5. 
Example
2: Subtract 3  (5). 
Example
3: Subtract . 

*Rewrite as addition
*Mult. top and bottom of 1st
fraction
by 2 and 2nd by 3 to get the
LCD of
6
*Take the difference of the
numerators and write over common denominator 6

The difference between 14/6 and 3/6 is 11/6 and the
sign of 14/6 (the
larger absolute value) is . That is how we get the answer
11/6 
Example
4: Simplify . 

*Exponent
*Multiply
*25  8 = 17

Example
5: Simplify 

*Eval. inside absolute value
*Exponent
*Multiplication
*7 + 6 = 13
*13  15 = 2

Example
6: Evaluate the expression
if x = 2 and y = 5. 
Plugging 2 for x and 5
for y and
simplifying we get: 

*Plug in 2 for x and 5 for y
*Rewrite num. as addition of
opposite
*Add
*Simplify fraction

Example
7: Is 1 a solution of  x + 4 = 6 + x? 
Replacing x with 1 we get: 

*Plug in 1 for x
*Take the opposite of 1
*Add 
Is 1 a solution?
Since we got a TRUE statement (5 does in fact
equal 5), then 1
is a solution to this equation. 
Practice Problems
These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.
In fact there is no such thing as too much practice.
To get the most out of these, you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem. At the link you will find the answer
as well as any steps that went into finding that answer. 
Practice
Problems 1a  1b: Subtract.
Practice
Problems 2a  2b: Simplify.
Practice
Problem 3a: Evaluate the expression when
x = 2 and y = 2.
Practice
Problem 4a: Is 2 a solution to the given
equation?
Need Extra Help on these Topics?
Last revised on July 24, 2011 by Kim Seward.
All contents copyright (C) 2001  2011, WTAMU and Kim Seward. All rights reserved.
