Algebra Lesson 11 – Additive Inverses
by Elaine Ernst Schneider
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
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