**Learning Objectives**

After completing this tutorial, you should be able to:

- Add real numbers that have the same sign.
- Add real numbers that have different signs.
- Find the additive inverse or the opposite of a number.

** Introduction**

This tutorial reviews adding real numbers as well as
finding the additive
inverse or opposite of a number . **I have the utmost
confidence
that you are familiar with addition**, **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.

** Tutorial**

**Step 2: Attach
their common sign
to sum.**

In other words:

If both numbers that you are adding are positive, then you will have a positive answer.

If both numbers that you are adding are negative then you will have a negative answer.

** Example
1:** Add -6 + (-8).

The sum of the absolute values would be 14 and their
common sign is
-. **That is how we get the answer of -14. **

**You can also think of this as
money.
I know we can all relate to that. ** Think of the
negative
as a loss. In this example, you can think of it as having lost 6
dollars and then having lost another 8 dollars for a **total loss of
14
dollars.**

The sum of the absolute values would be 14.2 and their
common sign is
-. **That is how we get the answer of -14.2.**

**You can also think of this as
money - I know
we can all relate to that. ** Think of the negative as a
loss. In this example, you can think of it as having lost 5.5
dollars
and then having lost another 8.7 dollars for a** total loss of 14.2
dollars.**

**Adding Real Numbers **

**with Opposite Signs**

**Step 2: Attach the
sign of the number
that has the higher absolute value.**

If the number with the larger absolute value is negative, then your sum is negative. In other words you have more negative than positive.

If the number with the larger absolute value was positive, then your sum is positive. In other words you have more positive than negative.

The difference between 8 and 6 is 2 and the sign of 8
(the larger absolute
value) is -. **That is how we get the answer of -2. **

**Thinking in terms of money: **we
lost
8 dollars and got back 6 dollars, so **we are still in the hole 2
dollars.**

***Take the difference of the
numerators**
**and write over common denominator 6**

***Reduce fraction**

The difference between 4/6 and 1/6 is 3/6 = 1/2 and the
sign of 4/6
(the larger absolute value) is +. **That is how we get the
answer
of 1/2.**

**Thinking in terms of money: **we
had
2/3 of a dollar and lost 1/6 of a dollar, so we would come out ahead
1/2
of a dollar.

Note that if you need help on fractions, go back to **Tutorial
3: Fractions.**

In this example, we are needing to combine more than
two numbers together,
but we will still follow the same thought process we do if there are
only
two numbers. I’m going to go ahead and step us through it going left to
right.

In this addition problem, we have some absolute values
thrown into
the mix. Remember that we need to do what is inside the absolute
values (grouping symbol) first and then add those numbers together. If
you need a **review on order of
operations go to Tutorial 4: Introduction to Variable Expressions and
Equations.**

The opposite of *x* is the
number -*x*.

Keep in mind that the opposite of 0 is 0.

**The following is an illustration of opposites using
the numbers 3
and -3:**

**For every real number a, **

When you see a negative sign in front of an expression,
you can think
of it as taking the opposite of it. For example, if you had
-(-2),
you can think of it as the opposite of -2. Since a number can
only
have one of two signs, either a '+' or a '-', then the opposite of a
negative
would have to be positive. So, -(-2) = 2.

** Example
7: **Write the additive inverse or opposite of
1.5.

When you have a negative in front of a parenthesis like
this, it is
another way to write that you need to find the additive inverse or
opposite.

Since the opposite of a negative is a positive, **our
answer is 10.**

-|-5.2| =

-(5.2) =

-5.2

-(5.2) =

-5.2

** 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 - 1d:Add.

1a. -15 + 7

(answer/discussion to 1a)

(answer/discussion to 1a)

1c. 3.2 + (-1.3) + (- 4.1)

(answer/discussion to 1c)

(answer/discussion to 1c)

Practice Problems 2a - 2b: Find the additive inverse or opposite.

2b. -20

(answer/discussion
to 2b)

Practice Problems 3a - 3b:Simplify.

3a. -(- 4)

(answer/discussion to 3a)

(answer/discussion to 3a)

** Need Extra Help on these Topics?**

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

This webpage covers how to add integers.

**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.