1. Math 8 Unit 2: Integers

2. What you’ll learn: Multiply and divide integers Use the order of operations with integers Solve problems involving integers

3. Unit 2: Integers Why its important: Used with temperature (negative temperatures is where water freezes) Used with finance (losing money is negative)

4. 2.1 USING MODELS TO MULTIPLY INTEGERS Unit 2: Integers

5. 2.1 Using Models to Multiply Integers Focus: Use a model to multiply two integers

6. 2.1 Using Models to Multiply Integers Remember that integers are positive and negative whole numbers. http://img.sparknotes.com/figures/5/50ca5e7 84bb7e4242910d5b8a571d103/number_line.g if

7. 2.1 Using Models to Multiply Integers Review addition of integers When adding positive numbers go right +2 + + 3= -2 + + 3 =

8. 2.1 Using Models to Multiply Integers Review addition of integers When adding negative numbers go left +2 + - 3= -2 + - 3 =

9. 2.1 Using Models to Multiply Integers Review subtraction of integers When subtracting positive numbers go left +2 - + 3= -2 - + 3 =

10. 2.1 Using Models to Multiply Integers Review subtraction of integers When subtracting negative numbers go right +2 - - 3= -2 - - 3 =

11. 2.1 Using Models to Multiply Integers Remember Multiplication is fast addition 2 x 5 is the same as 2 + 2 + 2 + 2 + 2 or 5 + 5 3 x 4 is the same as 3 + 3 + 3 + 3 or 4 + 4 + 4 2 x – 5 is the same as -5 + -5 - 3 x 4 is the same as – 3 + - 3 + - 3 + -3

12. 2.1 Using Models to Multiply Integers Write out the following multiplications as additions and solve 3 x -2 4 x – 3 5 x – 4 -3 x 2 -4 x 3

13. 2.1 Using Models to Multiply Integers Write out the following multiplications as additions and solve 3 x -2= -2 + - 2 + -2= -6 4 x – 3= -3 + - 3 + - 3 + -3= -12 5 x – 4= - 4 + -4 + -4 + -4 + -4 = -20 We can’t make add negative times so reverse the number pattern -3 x 2 = - 3 + -3= -6 -4 x 3= - 4 + - 4 + - 4= -12

14. 2.1 Using Models to Multiply Integers Homework

16. 2.2 DEVELOPING RULES TO MULTIPLY INTEGERS Unit 2: Integers

17. 2.2 Developing Rules to Multiply Integers Focus: Use patterns to develop rules for multiplying integers

18. 2.2 Developing Rules to Multiply Integers Fill in the highlighted part of the following table 0x4=1x4=2x4=3x4=4x4= 0x3=1x3=2x3=3x3=4x3= 0x2=1x2=2x2=3x2=4x2= 0x1=1x1=2x1=3x1=4x1= 0x0=1x0=2x0=3x0=4x0= 0x=1x =2x =3x =4x = 0x-2=1x =2x =3x =4x = 0x-3=1x =2x =3x =4x =

19. 2.2 Developing Rules to Multiply Integers 0x4=01x4=42x4=83x4=12 0x3=01x3=32x3=63x3=9 0x2=01x2=22x2=43x2=6 0x1=01x1=12x1=23x1=3 0x0=01x0=02x0=03x0=0 0x=1x =2x =3x = 0x-2=1x =2x =3x = 0x-3=1x =2x =3x = What pattern do you notice about the numbers as we go down the columns? Fill in the rest of the column following the patterns going down.

20. 2.2 Developing Rules to Multiply Integers 0x4=01x4=42x4=83x4=12 0x3=01x3=32x3=63x3=9 0x2=01x2=22x2=43x2=6 0x1=01x1=12x1=23x1=3 0x0=01x0=02x0=03x0=0 0x=01x = 2x =-23x=-3 0x-2=01x = 2x =-43x-2=-6 0x-3=01x = 2x =-63x-3=-9 Check your answers. What is the pattern going right to left?

21. 2.2 Developing Rules to Multiply Integers -3x4=-2x4=x4=0x4= -3x3=-2x3=x3=0x3= -3x2=-2x2=x2=0x2= -3x1=-2x1=x1=0x1= -3x0=-2x0=x0=0x0= -3x=-2x= x =0x = -3x-2= x =x-2=0x = -3x =-2x-3=x-3=0x = Use the pattern to fill in the rest of the table.

22. 2.2 Developing Rules to Multiply Integers -3x4=-12-2x4=-8x4=-40x4=01x4=42x4=83x4=12 -3x3=-9-2x3=-6x3=-30x3=01x3=32x3=63x3=9 x2=-6-2x2=-4x2=-20x2=01x2=22x2=43x2=6 -3x1= -2x1= x1= 0x1=01x1=12x1=23x1=3 -3x0=0-2x0=0x0=00x0=01x0=02x0=03x0=0 -3x=3-2x=2 x =10x =01x = 2x =-23x=-3 x-2=6 x =4x-2=20x =01x = 2x =-43x-2=-6 -3x =9-2x-3=6x-3=30x =01x = 2x =-63x-3=-9 Positive multiplied by a positive = Positive multiplied by a negative = Negative multiplied by a negative = Check your answers.

23. 2.2 Developing Rules to Multiply Integers Use your rules to solve: Practice: a.+4 x -5 = b.-3 x +6 = c.-2 x -8 = d.+5 x + 6 =

24. 2.2 Developing Rules to Multiply Integers The same rules apply to addition and subtraction + 2 + + 3 is the same as 2 + 3 + 2 + - 3 is the same as 2 – 3 + 2 - + 3 is the same as 2 – 3 + 2 - - 3 is the same as 2 + 3

26. 2.3 USING MODELS TO DIVIDE INTEGERS Unit 2: Integers

27. 2.3 Using Models to Divide Integers Focus: Use a model to divide integers

28. Division is the opposite of multiplication 8 ÷ 2 = 4 dividend factor quotient 4 x 2 = 8 factor product divisor

29. Investigate

31. 2.4 DEVELOPING RULES TO DIVIDE INTEGERS Unit 2: Integers

32. 2.4 Developing Rules to Divide Integers Focus: Use patterns to develop the rules for dividing integers

33. 2.4 Developing Rules to Divide Integers Remember the rules for multiplying integers: Positive multiplied by a positive is positive Positive multiplied by a negative is negative Negative multiplied by a positive is negative Negative multiplied by a negative is positive Same signs are positive Opposite signs are negative

34. 2.4 Developing Rules to Divide Integers Practice: a.+ 48 ÷ + 8 = b.+ 56 ÷ - 8 = c.- 42 ÷ + 6 = d.-36 ÷ - 6 =

35. 2.4 Developing Rules to Divide Integers Homework

37. 2.5 ORDER OF OPERATIONS WITH INTEGERS Unit 2: Integers

38. 2.5 Order of Operations with Integers Focus: Apply the order of operations to integers

39. 2.5 Order of Operations with Integers Remember Order of operations: B E D M A S

40. 2.5 Order of Operations with Integers Remember Order of operations: Brackets Exponents Division Multiplication Addition Subtraction } } Done at the same time from left to right

41. 2.5 Order of Operations with Integers Scientific calculators do order of operations for you. Check by doing the following: 8 + 2 x 3

42. 2.5 Order of Operations with Integers Practice = -10 ÷ 5 x - 2 ÷ 2 x - 3

43. 2.5 Order of Operations with Integers Practice = -10 ÷ 5 x - 2 ÷ 2 x – 3 = -2 x - 2 ÷ 2 x – 3 = - 4 ÷ 2 x – 3 = - 2 x – 3 = 6

44. 2.5 Order of Operations with Integers Practice a.-5 x 2 + 3 b.(-5 x 2) + 3 c.-5 x (2 + 3) d.2 + 3 x – 4 e.(2 + 3) x – 4 f.2 + (3 x – 4) =-7 =-25 =-10 =-20 =-10

45. 2.5 Order of Operations with Integers Homework