Download Integers and Absolute Value

Unit 1: Operations with Rational Numbers
Integers and Absolute Value
MCC7.NS.1b ~ Understand p + q as the number located a distance │q│from
p, the positive or negative direction depending on whether q is positive or
negative. Show that a number and its opposite have a sum of zero (0) (are
additive inverses). Interpret sums of rational numbers by describing realworld contexts.
Why is it useful for me to know the absolute value of a number?
The number one less than zero would be written as -1. This is an example of
a negative number. A negative number is a number less than zero. Negative
numbers are members of the set of integers. Integers are the set of all
positive and negative whole numbers and can be represented as points on a
number line.
Examples: Write integers that describes the situation.
Loss of 8 yards
4º rise in temperature
50-foot drop in altitude
Debt of $500
Deposit of $70
Gain of 10 pounds
To graph a particular set of integers, locate the integer points on a number
line. The number that corresponds to a point on the number line is called the
coordinate of the point.
Example: Name the coordinates of A,B,C, and D
A
-7
-6
-5
-4
D
-3
-2
C
-1
0
B
1
2
3
4
5
6
7
Absolute Value refers to the distance a number is from zero on the number
line. The symbol for absolute value is two vertical bars on either side of a
number (| # |).
Examples: Find the absolute value of the following numbers.
|7|
|-7 |
-|8|
- | -8 |
| 12 |
| -54 |
- | -25 |
Absolute values can also be found in equations.
1. Treat absolute value symbols like parenthesis . . . take the absolute
value first.
2. Perform indicated operation.
Examples: Simplify.
| 4 | - | -2 |
| -8 | + | -3 |
| -7 | • | -11 |
| -36| ÷ | -9 |
Examples: Evaluate each expression if a = 0, b =2, and c = -4
ab + |-30|
|c| - b
|b| ∙ |c| + |a|