Algebra Lesson #10 – Absolute Values
by Elaine Ernst Schneider
Pre Class Assignment: Completion and/or review of Algebra Lesson 9
Resources/Equipment/Time Required:
Outline:
In lesson 9, we learned about negative and positive numbers by using a number line. Negatives go left from the zero, and positives are counted off to the right. To add a negative and a positive, you start at one of the numbers and then count either to the left or the right depending on the sign. For example, to add -2 and 3, you can start at -2 and count to the right three places. You would end up at 1. -2 + 3 = 1
There is a term that is used in math to represent the distance that a number is from zero. That term is absolute value. The absolute value of 3 is three. The absolute value of -6 is six. This means that in terms of absolute value, -6 is larger than 3. In other words, 6 takes up more places on the number line. Look at the number line below. The red numbers represent the numbers of places it takes to reach -6 from zero. The blue color represents three. You can see that the red line is much longer than the blue one.
/_____/ _____/_____/_____/_____/_____/_____/_____/_____/_____/_____ /_____/
-6 … -5 …… -4 ….. -3 ….. -2 ….. -1 ….. 0 .…. 1 …… 2 …… 3 …….4 …… 5 ..…. 6
The concept of absolute value is important when adding positive and negative numbers. For example, if you have -7 + 4, you may wonder which number to use to begin the addition process. The number four is positive, so you might think that it represents “more.” Anyone would rather have $4 in their checking account that be in the hole $-7; right?! But in order to do the math, we must concern ourselves only with absolute value. The absolute value of seven is greater than the absolute value of four. Therefore, we begin with -7 and treat it as the larger number.
Here’s the problem:
-7 + 4 =
Subtract the values. 7 – 4 = 3. To determine which sign to use, you must consider absolute value. Since 7 is larger in absolute value, its sign will dominate. The answer will be -3.
-7 + 4 = -3
Suppose you have two negative numbers:
-7 + -2
Add the values. 7 + 2 = 9. Since you added absolute values, the answer is – 9.
-7 + -2 = -9
Assignment(s) including Answer key:
Now you try:
- -7 + -9
- -7 + 9
- -6 + 5
- -2 + -5
- -5 + 4
- – 3 + -5
- -5 + 2
- -15 + 6
- -17 +22
- -4 + -21
CUT HERE_________________________________________________________________
ANSWERS:
-
- -16
- 2
- -1
- -7
- -1
- -8
- -3
- -9
- 5
-25
Pre-Requisite To: Algebra Lesson 11
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