1. Integers

2. SOL Objective 7.3 The student will -
a. model addition, subtraction, multiplication and division of integers; and
b. add, subtract, multiply and divide integers.

3. Integers -4 -3 -2 -1 0 1 2 3 4 The set of integers:
{…, -4, -3, -2, -1, 0, 1, 2, 3, 4,…}
Negative integers are integers that are less than zero.
Positive integers are integers that are greater than zero.
Zero is neither positive or negative.
Negative Integers
Positive Integers

4. Absolute Value -4 -3 -2 -1 0 1 2 3 4 |3| “the absolute value of 3”
Two numbers are opposites if they are the same distance from 0 on a number line and are on opposite sides of 0.
3 and -3 are opposites
Absolute Value
|3| “the absolute value of 3”
“How far away am I from zero?”

5. How would you use an integer to write…
1. a bank deposit of $250
feet below sea level
3. a gain of 12 yards
4. a bank withdrawal of $50
5. a loss of 3 yards
6. an altitude of 4,750 feet
seconds before launch

6. Write these numbers in order,
from least to greatest
, |-2|, 3, |-4|
2. |4|, |-3|, 2, 1 -4 -3 -2 -1 1 2 3 4

7. Adding Integers Use number chips Use a number line Use addition rules
Link -4 -3 -2 -1 1 2 3 4

8. Adding Integers Addition Rules
Same Signs: the sum of two positive integers is positive
the sum of two negative integers is negative
Add the absolute values and use the same sign for the answer
2 + 4 = 6
|-2| + |-6|
= 8
-2 + (-6)
= -8

9. Adding Integers Addition Rules Different Signs:
find the difference of the absolute values
give the answer the same sign as the greater absolute value
5 + (-6)
|5| |-6|
6 – 5 = 1
= -1
Subtract the smaller number from the larger number
Give the answer the same sign as the greater absolute value

10. Adding Integers Addition Rules Different Signs: drop the signs
subtract the smaller number from the bigger number
steal the sign from the bigger number
5 + (-6)
6 – 5 = = - 1 1

11. Adding Integers Addition Rules Opposites:
any number added to its opposite equals zero
5 + (-5) = 0
= 0

12. WE DON’T! Keep Change Opposite Subtracting Integers
How do we subtract integers like: -2 – 5?
WE DON’T!
We turn them into addition problems…
we add its opposite
by using KCO
Keep
Change
Opposite

13. Subtracting Integers
K C O
= -7 -2 + -5
-2 + (-5) = -7

14. Subtracting Integers 4 – 7 = -4 – 7 = 4 – (-7) = -4 – (-7) =
4 + (-7) = -3
KCO
-4 + (-7) =
-11
KCO
4 + 7 = 11
KCO = 3
KCO

15. Multiplying Integers When you multiply… the answer is always…
two positive integers
positive
two negative integers
positive
a positive and a negative integer
negative
a negative and a positive integer
negative
4 • 5 = 20
-4 • -5 = 20
4 • -5 = -20
-4 • 5 = -20
If the signs are the same, the answer’s positive
If the signs are different, the answer’s negative

16. Multiplying Integers Evaluate xyz when x = 2, y = -4,and z = 6
Substitute
&
Simplify
= -8(6)
= -48
Evaluate a2 when a = -3
a2 = (-3)2
= -3 • (-3)
= 9

17. Multiplying Integers -xyz - ( )( )( ) -2 -4 6 - (8) (6) - (48) = -48
Evaluate -xyz when x = -2, y = -4,and z = 6
-xyz -
( )( )( ) -2 -4 6 -
(8)
(6) -
(48)
= -48

18. (-2)(-2)(3)(-2)(-1)(-1)(-1)(-1)(-2)(2)
(-2)(2)(5)(-1)(-1)(-1)
(-2)(-2)(3)(-2)(-1)(-1)(-1)(-1)(-2)(2)

19. Dividing Integers Use the same rules for division
that you use for multiplication
20 ÷ 5 = 4
-20 ÷ -5 = 4
If the signs are the same, the answer’s positive
20 ÷ -5 = -4
-20 ÷ 5 = -4
If the signs are different, the answer’s negative