**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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