Lesson Tutor : Algebra Lesson 11 – Additive Inverses

/  Lesson Tutor : Algebra Lesson 11 – Additive Inverses

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

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)]

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