Chapter 2 INTEGERS. There will be NO CALCULATORS used for this unit!

Transcription

1 Chapter 2 INTEGERS There will be NO CALCULATORS used for this unit!

2 2.2

3 What are integers? 1. Positives 2. Negatives Whole Numbers They are not 1. Not Fractions 2. Not Decimals

4

5 What Do You Know?! Can You Find Any Rules?

6 Multiplying two integers gives us a (+) x (+) = (-) x (+) = (+) x (-) = (-) x (-) =

7 Rules we need to remember Same signs Opposite signs POSITIVE product NEGATIVE product

8 (+3 ) x (+9) Their signs are the same, so the product is positive. Answer = +27 (-3 ) x (-9) Their signs are the same, so the product is positive. Answer = +27 (+3 ) x (-9) Their signs are the different, so the product is negative. Answer = -27 (-3 ) x (+9) Their signs are the different, so the product is negative. Answer = -27

9 Multiplication Properties ZERO Property: anything multiplied by zero is zero Example: 2 x 0 = 0 This means there are 2 groups of 0 We still have 0! OR We have 0 groups of 2...Still nothing there!

10 2. Identity Property Multiplying a number by 1, the product will be that same number. Example: 5 x 1 = 5 5 Groups of 1 1 group of 5 OR

11 3. Commutative Property 4 x 2 = 2 x 4 8 = 8 **order does not matter...

12 4. Distributive Property Example: 4(5 + 1) 4 Groups of (5+1) 4 Groups of 5 and 4 Groups of and 1 are SHARING the 4 *This means SHARING

13 Find the product! 1. (+50) X (-32) = 2. (+70)(-47) =

14 3. (-90) X (-52) = Challenge!!

15

16 Review from last class... (+) x (+) = (-) x (+) = (+) x (-) = (-) x (-) =

17 Review The product of two integers is 144. The sum of the integers is 7. What are the two integers?

18 Why does this work?! Double Negative = Positive

19 Work with a partner: How would you show 3 x 2 on a number line? Show it. INVESTIGATE We can do this with negative numbers too! See if you can demonstrate what 3 x (-2) looks like on a number line. What about (-3) x 2?

20 Number Line Models Review: How do number lines work?

21 (#) X (#) "tells us which way to face" and how many jumps + ---> face forward - ---> face backward how big the jumps are and tells us if we move forward or backwards + ---> forward - ---> backward

22 Example 1 (+3) (+5) (#) X (#) "tells us which way to face" and how many jumps how big the jumps are and tells us if we move forward or backwards

23 Example 2 (-2) X (4)

24 Example 3 (-4) X (-3)

25 Example 4 (3) X (-4)

26 Example 5

27 Steps for multiplying with tiles Think of a bank. 1. Our bank must start at zero. 2. First integer tells us what we are doing. a) If my first integer is positive, I am putting into the bank. This also tells me how groups to put in. b) If my first integer is negative, I am taking out of the bank. This also tells me how many groups to take out. 3.My second integer tells me what is in each group.

28

29 Example 1. (4) x 3 Example 2. 4 x (-3) Example 3. (-4) x(-3) Example 4. (-4) x 3

30

31 2.4

32 Review 6 x (-2) Show the answer using tiles AND a number line

33 INVESTIGATE How are multiplication and division related Choose 1 positive integer and 1 negative integer. Express each integer as a product. For each product, write two related division facts.

34 Means Opposite Division is the INVERSE of Multiplication... But the SAME rules apply

35 The Rules to the Game!! (+) (+) = (-) (+) = (+) (-) = (-) (-) =

36 (+63) (+7) = (-63) (+7) = (+63) (-7) = (-63) (-7) =

37 We already know that when two numbers are multiplied together... the answer is called a product When two numbers are divided...the answer is called a...>>>>>>>

38 = 25 Dividend Divisor Quotient We can also write division as a fraction.. (125) (5) = 25 The fraction bar is a grouping symbol. We are DIVIDING 125 into 5 groups. **There are hidden brackets!

39 Example 1. (-15) 3 = Example 2. (-54) (-9) =

40 Find the divisor Example = 10

41 Emma made withdrawals of $17 from her bank account. In total she withdrew $204. How many times did she withdraw?

42

43

44 Dividing with Tiles The bank needs to start with zero in it. 1. The bank is to end up containing the dividend If we put in groups, our quotient will be positive. If we take out groups, our quotient will be negative. 2. Our answer is how many groups we have either put in or taken out to end up with the correct amount of tiles needed. 3. When the signs are the same, we can put in to the bank to model the quotient. 4. When the signs are opposite, we have to make zero pairs in order to model the quotient.

45

46 # divide # End goal direction you move and how many are in each jump! *When the divisor is positive, we move forward on the number line *When the divisor is negative, we move backwards on the number line

47 Using a number line model 6 2 How many steps of 2 does it take to get to 6?

48

49

50

51

52

53

54

55 BEDMAS!!! B= Brackets E= Exponents D= Division M= Multiplication A= Addition S= Subtraction

56 Skill Testing Question (3 x 50) 20 5=

57 Where should the Brackets go?? 9 x SOLVE!

58 Example x (8-5)

59 Example 3 (14 5) (9 6)

60 Example 4 (36-3 x 4) (15-9 3)

61 Example 5 5 x x 2

62 Example 6

63 Example 7

64 Example 8