1. R.5-Multiplication with whole numbers and area
Catherine Conway
Math 081

2. Multiplying Whole numbers
Multiplication is a faster form of addition.
Notation 3
x 4
3 · 4
3 x 4
(3) 4
(3)(4)
3(4)
If a number is next to a letter (variable) it also represents multiplication
3n means 3 time n
ab means a times b
See table on pg 44

3. Table on page 44

4. Vocabulary and Properties
Product – indicates multiplication
Factors – the numbers you are multiplying together
Distributive Property
If a, b, and c represent any three whole numbers, then
a(b + c) = a(b) + a(c)

5. Multiplication with whole numbers
Multiplying using the distributive property
Example:
4(5 + 8)
4(5) + 4(8)
Distributive Property – distribute 4 to 5 and 4 to 8
Multiply – 4 x 5 = 20, 4 x 8 = 32 52
Add – ( ) = 52

6. Multiplication of Whole Numbers
Multiplying using the distributive property
Multiplying a 2 digit number by 1 digit number
Multiply 6 and 54
Method 1: Column method
Method 2: Using Distributive Property 2 54
x 6
6(54) = 6(50 + 4)
= 6(50) + 6(4) 32 4 =
= 324

7. Multiplication of Whole Numbers
Multiplying a 2 digit number by 2 digit number
Multiply 25 and 32
Method 1: Column method
Method 2: Using Distributive Property 25
x32
25(32) = 25(30 + 2) 25
x30 75 25
x 2 5
= 25(30) + 25(2) 5 =
+75
= 800
800
You try: pg 53 #23, 24

8. You try: pg 53 #23, 24 1 4 4 2 34 5 16 2
+13 8
+ 8 1
1725
972

9. Multiplication of Whole Numbers
Multiplying a 3 digit number by 3 digit number
Multiply 162 and 317
Method 1: Column method
Method 2: Using Distributive Property
162(317) = 162( )
162
x317
= 162(300)+162(10)+162(7)
You try: pg 53 #39
= 48, , ,134
1,134
1,620
= 51,354
48,600
162
x300
48,600
162
x 10
1,620
162
x 7
1,134
51,354

10. Application – pg 47 Example 7

11. Application – pg 47 Example 8

12. Application – pg 48 Example 9
SOLUTION:
Reading toward the top of the label, we see that there are about 32 chips in one serving, and approximately 3 servings in the bag. Therefore, the total number of chips in the bag is
3(32) = 96 chips.
This is an approximate number, because each serving is approximately 32 chips. Reading further we find that each serving contains 160 calories. Therefore, the total number of calories consumed by eating all the chips in the bag is
3(160)=480 calories.

13. Application – pg 48 Example 10
Practice: pg 56 #104, 104, 107
Application – pg 48 Example 10
SOLUTION:
Each hour of bowling burns 265 calories. If the person bowls for 2 hours, a total of
2(265) = 530 calories
Will have been burned. Because a bag of chips contains only 480 calories, all of them have been burned with 2 hours of bowling.

14. Area
Area measures the amount of surface the object has.
For example: The amount of paint to cover a wall.
Area of a square: s x s (side x side)
Area of a rectangle: l x w (length x width)
Composition figures are figures that are made up of more than 1 shape. s w l

15. Find the total Area of the house

16. R.6-Division with whole number
Math 081
Catherine Conway

17. Division with whole numbers
Vocabulary:
Divisor – the number used to divide
Dividend – the number being divided
Quotient – indicates division, the answer you get when you divide
Notation: 19 30 5 ) 38 2
20÷4 =5 =6
35/7 =5
See table on page 60 for wording of division questions

18. What does it mean to divide?
What do we multiply the divisor by to get the dividend?
For example, what is the quotient of 45 and 9?
Think: What do we multiply 9 (the divisor) by to get 45 (the dividend)?
45 ÷ 9 = ? means 9 · ? = 45
9 · 5 = 45
45 ÷ 9 = 5

19. Division by 1 digit number
Example: 675 ÷ 5 What do I need to multiply 5 by to get 675? Or How many times can 5 go into 675? 1 3 5 )
6 7 5 5 5 1 7 15 2 5
2 5
You Try: pg 67 #23, 25, 34

20. You Try: pg 67 #23, 25, 34
23) 360 ÷ 8
25) 138/6
34) 50,004 divided by 3

21. Division by 2 digit numbers
Example: 1872 ÷ 12 What do I need to multiply 12by to get 1872? Or How many times can 12go into 1872? 1 5 6 ) 12 12 6 7 60 7 2
7 2

22. You Try: pg 68 #48, 53

23. Division with remainder2, 8 7
R10 )
34,450 12
Sara has an annual income of $34, How much does she make each month? 24 1 4 96 8 5 84 1
You Try: pg 68 #63, 66
Challenge question: #71, 72 10

24. You Try: pg 68 #63, 66 Challenge question: #71, 72

25. Division by zero
CANNOT DIVIDE BY ZERO!!!! 30
=Ø (does not exist, DNE)

26. Estimating with Division
See pg 67 #35-38

27. Estimating with Division
See pg 67 # 1 2 2 4 4 2 6 3