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You are HERE >> Mathematics > Algebra > Grade 9

Algebra Lesson 11 - Additive Inverses
      by Elaine Ernst Schneider
    December 21, 2000

AMAZON PRODUCTS
Practical Algebra: A Self-Teaching Guide
Algebra to Go : A Mathematics Handbook
Algebra Unplugged

Objective(s): By the end of this lesson the student will be able to: 
identify any number's opposite and be able to add a negative number to a positive one.

Pre-Class Assignment: Review/ completion of Algebra Lesson 10
Resources/Equipment/Time Required: 
Outline:

Additive Inverses are opposites. Two numbers are opposites if their sum equals zero. For example, -8 and 8 are additive inverses because their sums total zero. This makes them opposites. 

Another way to write the opposite of 8 is to write (-8). To subtract a negative 8 is the same as making it a positive 8, or finding its opposite.

You can do the same thing with variables. For example, -(-x) = x.

Using this principle, let's add a negative number to a positive one: 8 + (-3) = 8 3 = 5. This could be read as 8 plus a negative 3 OR 8 minus 3 OR 8 plus the opposite of 3.

In algebra, subtracting a number can also be described as adding its opposite.

For example, x y = x + (-y).

OR

8 (-5) = 8 + 5 = 13
 
 

Now, let's turn things around a bit. Try this one:

14 28 = x

How can you rewrite that to use what you've learned about opposites?

14 + (-28) = x

14 = x
 
 

Let's try one more:

11 (-3) 4 = x

11 + 3 4 = x

14 4 = x

10 = x
 
 


Assignment(s) including Answer key: 
 

                                    1. 5 7 
                                    2. 8 (-10) 
                                    3. 3 7 
                                    4. 7 9 
                                    5. 7 + (-3) 
                                    6. 25 250 
                                    7. 5.8 2.3 
                                    8. 2.3 5.8 
                                    9. (34 13) (15 17) 
                                   10. 11 5 [6 + (-13)]
 
 

                                 Answer key:

                                    1. 2 
                                    2.  18 
                                    3. 10 
                                    4. 16 
                                    5. 4
                                    6. 225 
                                    7. 3.5 
                                    8. 3.5 
                                    9. 23 
                                   10 .13 


Pre-Requisite To:  Algebra Lesson 12


 
 
Submitted by:  Copyright© Elaine Ernst Schneider is a freelance writer and a teacher. She has been writing since high school and has published articles, songs, and children's work. Presently, Elaine is a curriculum author for Group Publishing and also writes the City Songs column for www.newcolonist.com ezine. 
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