1. Integers Rule! Dr. Deborah Santiago

2. What You Will Learn 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 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 is 9.

8. Negative Numbers Are Used to Measure Temperature

9. Negative Numbers Are Used to Measure Under 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 used car, but they had to get a loan from the bank for $5,000. When counting all their money they add in a -$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 +

12. Solve the problems on IXL or the worksheet provided.

13. Integer Addition Rules Positive + = Positive: 5 + 4 = 9 Negative + = Negative: - 7 + - 2 = - 9 Sum of a negative and a positive number: Use the sign of the larger number and subtract - 7 + 4 = -3 6 + -9 = - 3 - 3 + 7 = 4 5 + -3 = 2

14. Solve the Problems -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 -18 14 -13 7 11

15. Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 = -2 5 – 3 = 2 0 -4 1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

16. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. +-

17. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + -5 =-2

18. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +6 + -4 =+2

19. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 + - +3 + -7 =-4

20. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 - + -3 + +7 =+4

21. Solve the problems on IXL or on the worksheet provided.

22. Integer Subtraction Rules Keep, Change, Change, and then follow the Addition Rules! Negative - Positive = Negative: - 5 - 3 = -5 + -3 = -8 Positive - Negative = Positive + Positive = Positive: 5 - -3 = 5 + 3 = 8 Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double negatives to a positive) (-5) - (-3) = ( -5) + 3 = -2 (-3) - ( -5) = (-3) + 5 = 2

23. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8

24. Solve the problems on IXL or on the worksheet provided.

25. Integer Multiplication Rules Positive x Positive = Positive: 3 x 2 = 6 Negative x Negative = Positive: -2 x -8 = 16 Negative x Positive = Negative: -3 x 4 = -12 Positive x Negative = Negative: 3 x -4 = -12

26. Practice -10 x 3 = 10 x 3 = -10 x -3 = 10 x -3 =

27. Solve the problems on IXL or on the worksheet provided.

28. Integer Division Rules Positive ÷ Positive = Positive: 12 ÷ 3 = 4 Negative ÷ Negative = Positive: -12 ÷ -3 = 4 Negative ÷ Positive = Negative: -12 ÷ 3 = -4 Positive ÷ Negative = Negative: 12 ÷ -3 = -4

29. Practice -9 / 3 = 9 / 3 = -9 / -3 = 9 / -3 =

30. Solve the problems on IXL or on the worksheet provided.

31. Integers Rule!