1. Grade 8 Integers!

2. What You Will Learn Some definitions related to integers. Rules for multiplying and dividing integers. Are you ready??

3. Definition Positive number = a greater than zero. 0123456

4. Definition Negative number = a less than zero. 0123456-2-3-4-5-6

5. Definition Opposite Numbers = numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

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

7. 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 Level 0 10 20 30 -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 = -9 x -9 =

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

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 = -9 x 9 =

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

18. One Way to Multiply Integers Is With a Number Line 0123456-2-3-4-5-6 When the signs are the same, count to the right. When the signs are opposite, count to the left.2 x 3 = 6 +

19. One Way to Multiply Integers Is With a Number Line 0123456-2-3-4-5-6 (+3) x (-2) = -6

20. What about dividing with integers?

21. Integer Division Rule 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. Review what you think you know with a partner!