1. Interesting Integers!

2. What You Will Learn Are you ready??
Some definitions related to integers.
Rules for adding and subtracting integers.
A method for proving that a rule is true.
Are you ready??

3. Definition
Positive number – a number greater than zero. 1 2 3 4 5 6

4. Definition
Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

5. Definition
Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

6. Definition
Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7
opposite -7

7. |9| = 9 |-9| = 9 The absolute value of 9 or of –9 is 9. Definition
Absolute Value – The distance a number is from zero.
The absolute value of
9 or of –9 is 9.
|9| = 9
|-9| = 9

8. Integer Addition Rules
Rule #1 – If the signs are the same,
just add the numbers and keep the sign the same.
9 + 5 = 14
= -14

9. Integer Addition Rules
Rule #2 – If the signs are different, subtract the numbers and the answer gets the sign of the “bigger” number. =
Larger abs. value
Answer = - 4
9 - 5 = 4

10. One Way to Add Integers Is With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left. - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

11. One Way to Add Integers Is With a Number Line= -2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

12. One Way to Add Integers Is With a Number Line= +2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

13. One Way to Add Integers Is With a Number Line= -4 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

14. One Way to Add Integers Is With a Number Line= +4 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

15. Integer Subtraction Rule
Keep, Change, Change
Turns a subtraction problem into an addition problem. Then just follow the rules for addition.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!

16. Integer Multiplication and Division
Just do the math.
If the signs are the same, the answer is positive.
-2 • (-7) = 14
14 ÷ 7 = 2

17. Integer Multiplication and Division
Just do the math.
If the signs are different, the answer is negative.
-2 • 7 = -14
14 ÷ (-7) = -2

18. Order of Operations
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

19. Order of Operations To follow order of operations:
Check for parentheses. If you have any, solve for what is inside them.
Check for exponents. If you have any, find the value.

20. Order of Operations To follow order of operations:
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.

21. Properties of Numbers 4 + 5 + 6 = 6 + 4 + 5
Commutative Property – You can add or multiply numbers in any ORDER. =

22. Properties of Numbers (4 + 5) + 6 = 4 + (5 + 6)
Associative Property – When you add or multiply, you can GROUP the numbers in any combination.
(4 + 5) + 6 = 4 + (5 + 6)

23. Properties of Numbers 3 + 0 = 3 4 • 1 = 4 Identity Property –
You can add zero to any number and it will stay the same.
b) You can multiply any number by one and it will stay the same.
3 + 0 = 3
4 • 1 = 4

24. Properties of Numbers 2(3 – 4) = 2(3) – 2(4) = 6 – 8 = -2
Distributive Property – Multiply the number outside of the parentheses by each term inside the parentheses.
2(3 – 4) =
2(3) – 2(4) =
6 – 8 = -2

25. Aren’t integers
interesting?