Beginning Algebra
Tutorial 5: Adding Real Numbers
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
Adding Real Numbers
with the Same Sign

Step 1: Add the
absolute values.
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). 
6 + (8) = 14
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. 
Example
2: Add 5.5 + (8.7). 
5.5 + (8.7) = 14.2
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 1: Take the
difference of the absolute
values.
Step 2: Attach the
sign of the number
that has the higher absolute value.
Which did you have more of, negative or
positive?
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. 

Example
3: Add 8 + 6. 
8 + 6 = 2.
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. 
Example
4: Add . 

*Mult. top and bottom of first
fraction by 2 to get the LCD of 6
*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. 
Example
5: Add 10 + 7 + (2) + 5. 
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. 

* 10 + 7 = 3
*3 + (2) = 5

Example
6: Add . 

*Add inside the absolute values
*Evaluate the absolute values
*Add

Opposites are two numbers that are on opposite sides
of the origin
(0) on the number line, but have the same absolute value. In other words, opposites are the same distance away from the origin,
but
in opposite directions.
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:

Double Negative Property
For every real number a,
(a) = 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. 
The opposite of 1.5 is 1.5, since both of these
numbers have
the same absolute value but are on opposite sides of the origin on the
number line. 
Example
8: Write the opposite of 3. 
The opposite of 3 is 3, since both of these
numbers have the
same absolute value but are on opposite sides of the origin on the
number
line. 
Example
9: Simplify (10). 
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. 
Example
10: Simplify 5.2. 
5.2 =
(5.2) =
5.2 
*Evaluate the absolute value
*Find the opposite 
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.
Practice
Problems 2a  2b: Find the additive inverse or opposite.
Practice
Problems 3a  3b: Simplify.
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.




