**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**

*a - b = a + (-b) *

* or *

*a - (-b) = a + 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.

Subtracting 5 is the same as adding a -5.

Once it is written as addition, we just** follow
the rules for addition, as shown in Tutorial 5: Adding Real Numbers**,
to complete **for an answer of -8.**

Subtracting -5 is the same as adding 5.

Once it is written as addition, we just** follow
the rules for addition, as shown in Tutorial 5: Adding Real Numbers**,
to complete **for an answer of 2.**

***Mult. top and bottom of 1st
fraction**
**by 2 and 2nd by 3 to get the
**

***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**

Since we have several operations going on in this
problem, we will
have to use the order of operations to make sure that we get the
correct
answer.

If you need to **review
the order
of operations go to Tutorial 4: Operations of Real Numbers.**

***25 - 8 = 17**

Since we have several operations going on in this
problem, we will
have to use the order of operations to make sure that we get the
correct
answer.

If you need to **review
the order
of operations go to Tutorial 4: Operations of Real Numbers.**

***Exponent**

***Multiplication**

***7 + 6 = 13**

***13 - 15 = -2**

To review **evaluating
an expression
go to Tutorial 4: Introduction to Variable Expressions and Equations.**

**Plugging -2 for x and 5
for y and
simplifying we get:**

***Rewrite num. as addition of
opposite**

***Add **

***Simplify fraction**

If you need a **review on
what a solution to an equation is go to Tutorial 4: Introduction to
Variable
Expressions and Equations.**

**Replacing x with -1 we get:**

***Take the opposite of -1**

***Add**

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.

1a. -10 - (-2)

(answer/discussion to 1a)

(answer/discussion to 1a)

1b. - 4.1 - 5.3

(answer/discussion to 1b)

(answer/discussion to 1b)

Practice Problems 2a - 2b:Simplify.

Practice Problem 3a:Evaluate the expression whenx= 2 andy= -2.

Practice Problem 4a:Is -2 a solution to the given equation?

** Need Extra Help on these Topics?**

**http://www.mathleague.com/help/integers/integers.htm#subtractingintegers**

This webpage goes over subtracting real numbers.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 24, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.