1. 7/8 A Review and new concepts with Integers!

2. What You Will Learn Are you ready??
Some definitions related to integers.
Rules for multiplying and dividing integers.
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. The absolute value of 9 or of –9 = 9. Definition
Absolute Value = The size of a number with or without the negative sign.
The absolute value of
9 or of –9 = 9.

8. Negative Numbers Are Used to Measure Temperature

9. Negative Numbers Are Used to Measure Above and Below Sea Level30 20 10
-10
-20
-30
-40
-50

10. Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car but
had to get a loan from the bank for $5,000.
When counting all their money they add
in -$5,000 to show they still owe the bank.

11. Hint
If you don’t see a negative or positive sign in front of a number it is positive. 9
9 = +

12. Integer Multiplication Rules
Rule #1 – If the signs are the same, pretend the signs aren’t there. Multiply the numbers and then put a positive sign in front of your answer.
9 x 5 = +45
(-9) x (-5) = +45

13. Solve the Problems -3 x -5 = 4 x 7 = (+3) x (+4) = -6 x -7 = 5 x 9 =

14. Answers -3 x -5 = 4 x 7 = (+3) x (+4) = -6 x -7 = 5 x 9 = -9 x -9 =
+15
+28
+12
+42
+45
+81

15. Integer Multiplication Rules
Rule #2 – If the signs are different pretend the signs aren’t there. Multiply the numbers and put a negative sign in front of your answer.
-9 x 5 = -45

16. Solve These Problems 3 x -5 = -4 x 7 = (+3) x (-4) = -6 x 7 = 5 x -9 =

17. Answers 3 x -5 = -15 -4 x 7 = -28 (+3) x (-4) = -12 -6 x 7 = -42

18. One Way to Multiply Integers Is With a Number Line
When the signs are the same, count
to the right.
When the signs are opposite, count
to the left. 2 x 3 = 6 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

19. One Way to Multiply Integers Is With a Number Line
(+3) x (-2) = -6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

20. What about dividing with integers?

21. Integer Division Rule 14 ÷ (-7) is the same as -14 ÷ (+7) = -2
Dividing by a negative number is the same as multiplying by a negative number. Same signs result in a positive answer and different signs result in a negative answer.
14 ÷ (-7) is the same as
-14 ÷ (+7)
= -2

22. Here are some more examples.
16 ÷ (-8)= -2
16 ÷ (+8)= 2
-33 ÷ (-11)= 3
-33 ÷ (+11)= -3

23. How do we know that “A negative times (or divided by) a negative equals a positive” is true?
The following slides show two ways to think about it…

24. Think about grammar! Some people think of a negative as meaning “not”.
So if I say I’m not not going to the store, doesn’t that mean I AM going to the store?
(two negatives results in a positive answer?)

25. Think about patterns:
4 x 5 = 20
3 x 5 = 15
2 x 5 = 10
1 x 5 = 5
0 x 5 = 0
Both numbers are going down!

26. What about this pattern?:
4 x -5 = -20
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0
The left numbers are going down
and the right #s are going up!

27. But if we continue that pattern:
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0
-1 x -5 = 5
-2 x -5 = 10
-3 x -5 = 15
-4 x -5 = 20
The left #s are still going down
& the right #s are still going up!
(Neg x neg = positive)

28. You have learned lots of things
about multiplying and dividing
integers.