Download 2.1 Introduction to Integers

Math 100 Class Notes
2.1 Introduction to Integers
We compare integers just as we compare whole numbers. For any two numbers graphed on a
number line, the number to the right is the greater number and the number to the left is the
smaller number.
Example:
− <
< means “is less than”
means “− is less than ”
Insert <, > or =
1. −3
4
3.
−3
2. −7
0
−11
Example:
>
> means “is greater than”
means “12 is greater than 3”
5
6
R. Getso
Since the absolute value of a number is that number’s distance from 0, the absolute value of a
number is always 0 or positive. It is never negative.
| |=
|− | =
zero
Examples: Insert <, > or =
|11|
4. |−11|
5. −(−3)
7. |3|
8. |−8|
|−5|
a positive number
|−7|
6. −|−21|
−(−7)
−(−4)
9. −|−10|
−(−15)
5 is the opposite of –5 and –5 is the opposite of 5.
The opposite of 4 is − 4 and is written as −(4) = −4.
The opposite of −4 is 4 and is written as −(−4) = 4.
If is a number, then −(− ) = .
Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0.
Math 100 Class Notes
Examples: Simplify.
10. −(−27)
Evaluate.
14. |− |, = −7
11. −|−13|
12. |−17|
15. −|− |, = −21
13. −(−33)
16. | |, = −7
2.2 Adding Integers
Step 1: Add their absolute values.
Step 2: Use their common sign as the sign of the sum.
Step 1: Find the larger absolute value minus the smaller absolute value.
Step 2: Use the sign of the number with the larger absolute value as the sign of the sum.
7
8
R. Getso
If
is a number, then − is its opposite.
+ (− ) = 0
− +
=0
The sum of a
number and its
opposite is 0
Helpful Hint: Don’t forget that addition is commutative and associative. In other words, numbers
may be added in any order.
Examples: Simplify.
1. −2 + 3 − 7
2. −12 + 33 − 17
5. Evaluate
+
for
= 5 and
4. 29 − 10 − 3 + 17
3. −19 − 3 + 17
= −9
2.3 Subtracting Integers
If
and are numbers, then
−
=
+ (− ).
To subtract two numbers, add the first number to the opposite (called additive inverse) of the
second number.
Examples:
1. 7 − 4
5. 9 − 3 + (−5) − (−7)
2. −5 − 3
4. −8 − (−2)
3. 3 − (−6)
6. Evaluate
−
for
= −6 and
=8