1. Integers, Absolute Value & Integer Operations

2. Topics Covered Absolute Value Opposites Integer Operations
What are integers?
Absolute Value
Opposites
Integer Operations
Applications

3. What are integers?
The integers are the positive and negative whole numbers together with zero.
… -5 , -4 , -3 , -2, -1 , 0 , 1 , 2 , 3 , 4 , 5 , …

4. Absolute Value
Absolute Value: Is the distance between a number and zero on the number line.
Examples:
|12|
|-17|
|53|
-|47|
-|-19|

5. Try…
Find |-76|
Find |84|
Find -|-39|

6. Opposites
Opposites: Are numbers which are the same distance from zero on the number line but on opposite sides of zero.
Find the opposites of the following numbers 37
-42
-(63)
-(-78)

7. Adding Integers Same Sign (moving same direction along number line)
Positive + Positive = Positive
Negative + Negative = Negative
Opposite Signs (moving oppositive directions on number line)
Subtract & take the sign of the larger number
Examples: (-5) (-6)
(7) + (-10)

8. Try…
(-37) + (-42)
(-57) + (-213)
14 + (-15) (-42)

9. Translate from words to math
The sum of -23 and 49
The total of 3, -10, and 5
-5 added to the sum of -8 and 6

10. Application: Example #1
At midnight the temperature was -14 degrees Fahrenheit.
By noon, the temperature had risen 10 degrees.
What was the temperature at noon?

11. Application: Example #2
Ellen’s checking account balance is $23. If she writes a check
For $40, what is her new balance?

12. Try…
At 6:00AM the temperature was -4 degrees Fahrenheit. By noon, the temperature had risen by 12 degrees. What was the temperature at noon?
Jorge’s checking account is overdrawn. His beginning balance was -$56. If he deposits his paycheck for $389, what is his new balance?

13. Subtraction Rule for Integers
Change Subtraction to Addition (“Draw a Line, Change the Sign”)
Change the subtraction sign to an addition sign.
Change the sign of the number that follows to its opposite.
Examples:
27 – (-35)
-34 – (-8)
23 – 89
-17 – 43

14. Try…
18 - (-27)
-13 – (-35)
64 – (-37)
(-19) – 67

15. Translating Examples The difference of 70 and 98 150 decreased by 75
Subtract 10 from 16
22 less than - 90

16. Applications: Example #1
Temperatures on the moon range from -184 degrees Celsius
during its night to 214 degrees Celsius during its day. Find the
Difference between the highest and lowest temperature on
the moon.

17. Applications: Example #2
Jeff’s balance in his checking account was $2036 at the
Beginning of the week. During the week, he wrote two checks,
Made two deposits, and made one ATM withdrawal.
What is his ending balance?
Check
- $150
- $25
Paycheck
$480
ATM
- $200
Cash
$80

18. Rules for Multiplying or Dividing Integers
Same sign answer is positive
Different signs answer is negative
Would the following examples have positive or negative solutions?
(- n )( m ) (-1)(-1)(-1)
(-x )( -y) (-1)(0)(-1)
( a ) / ( - b ) (-10)(-10)(-10)(-10)

19. Try…
(-6)(5)
2 • -9
-3 x -5
(24) ÷ (-6)
−10 −2

20. Exponents An exponent represents repeated multiplication.
In the expression
The x is called the base and the n is called the exponent.
Some examples of exponents