1. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit…

2. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example :

3. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example : 1. Multiply 4 x 6

4. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example : 1.Multiply 4 x 6 = 24 2.Put 4 in the ones place of the answer, and carry your 2 on the tens place above the 5…

5. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example : 1.Multiply 4 x 6 = 24 2.Put 4 in the ones place of the answer, and carry your 2 on the tens place above the 5… 3.Multiply 4 x 5 and then add the 2 you carried…

6. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example : 1.Multiply 4 x 6 = 24 2.Put 4 in the ones place of the answer, and carry your 2 on the tens place above the 5… 3.Multiply 4 x 5 and then add the 2 you carried… 4 x 5 = 20 20 + 2 = 22

7. Multiplication and Division of Whole Numbers Let’s start by multiplying numbers that contain 2 or more digits by a single digit… For Example : 1.Multiply 4 x 6 = 24 2.Put 4 in the ones place of the answer, and carry your 2 on the tens place above the 5… 3.Multiply 4 x 5 and then add the 2 you carried… 4 x 5 = 20 20 + 2 = 22 4.Place the result next to the 4 in the answer

8. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example :

9. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5

10. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8

11. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8 = 40 2. Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row…

12. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8 = 40 2.Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row… 3.Now multiply 5 x 1 and then add 4

13. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8 = 40 2.Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row… 3.Now multiply 5 x 1 and then add 4 4.5 x 1 = 5, 5 + 4 = 9 : Place this result in the tens place of the answer…

14. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8 = 40 2.Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row… 3.Now multiply 5 x 1 and then add 4 4.5 x 1 = 5, 5 + 4 = 9 : Place this result in the tens place of the answer… 5.Multiply 3 x 5

15. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 1. Multiply 5 x 8 = 40 2.Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row… 3.Now multiply 5 x 1 and then add 4 4.5 x 1 = 5, 5 + 4 = 9 : Place this result in the tens place of the answer… 5.Multiply 3 x 5 = 15 6.Place in the answer…

16. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 7.Drop a zero into the ones place of the next line …

17. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 7.Drop a zero into the ones place of the next line … 8.3 x 8 = 24

18. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 7.Drop a zero into the ones place of the next line … 8.3 x 8 = 24 9.3 x 1 = 3, 3 + 2 = 5

19. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 7.Drop a zero into the ones place of the next line … 8.3 x 8 = 24 9.3 x 1 = 3, 3 + 2 = 5 10.3 x 3 = 9

20. Multiplication and Division of Whole Numbers Now we will multiply a three digit number by a two digit number… For Example : We will begin our multiplication by the number in the second row starting with the ones place… 5 7.Drop a zero into the ones place of the next line … 8.3 x 8 = 24 9.3 x 1 = 3, 3 + 2 = 5 10.3 x 3 = 9 11.Now add the numbers…

21. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6

22. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 - Since 2 can not divide 1, how many 2’s divide 15 without going over 15 ?

23. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 - Since 2 can not divide 1, how many 2’s divide 15 without going over 15 ? 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 - place in answer above the 5 2 x 8 = 16 7

24. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 Now multiply and subtract… 7 14 1

25. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 Drop the 6 for the next number to divide… 7 14 1 6

26. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 7 14 1 6 - how many 2’s divide 16 ?

27. Multiplication and Division of Whole Numbers Now Long Division… we’ll start out easy… 2 ) 1 5 6 7 14 1 6 8 1 6 0 - Multiply and subtract to find remainder…

28. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) :

29. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : - 11 can not divide 10, how many 11’s divide 104 without going over 104 ?

30. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : - 11 can not divide 10, how many 11’s divide 104 without going over 104 ? 11 x 9 = 99 - place in answer above the 4 11 x 10 = 110 9

31. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : - Now multiply and subtract 9 9 9 5

32. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : - Bring down the next digit 9 9 9 5 5

33. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : 9 9 9 5 5 - how many 11’s divide 55 without going over 55 ?

34. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : 9 9 9 5 5 -how many 11’s divide 55 without going over 55 ? -11 x 5 = 55 ( place in answer ) 5

35. Multiplication and Division of Whole Numbers 1 1 ) 1 0 4 5 EXAMPLE # 2 (division ) : 9 9 9 5 5 5 5 5 0 - Now multiply and subtract

36. APPLICATION PROBLEMS EXAMPLE : An offset press feeds at the rate of 140 impressions every hour. How many impressions are made in 4 hours ?

37. APPLICATION PROBLEMS EXAMPLE : An offset press feeds at the rate of 140 impressions every hour. How many impressions are made in 4 hours ? Multiply 140 x 4 We have a given rate of production given over a certain time frame. That rate multiplied by the number of time frames will give total production.

38. APPLICATION PROBLEMS EXAMPLE : An offset press feeds at the rate of 140 impressions every hour. How many impressions are made in 4 hours ? Multiply 140 x 4 140 x 4 0 65 560 impressions

39. APPLICATION PROBLEMS EXAMPLE #2 ( applications ): A welder fabricates 35 steel water tanks for a price of $9,940.00. How much is each water tank cost to produce ?

40. APPLICATION PROBLEMS EXAMPLE #2 ( applications ): A welder fabricates 35 steel water tanks for a price of $9,940.00. How much is each water tank cost to produce ? Divide $9,940 by 35 When you are finding a per item cost, you will always divide the total dollars spent by the number of items produced.

41. APPLICATION PROBLEMS EXAMPLE #2 ( applications ): A welder fabricates 35 steel water tanks for a price of $9,940.00. How much is each water tank cost to produce ? Divide $9,940 by 35 When you are finding a per item cost, you will always divide the total dollars spent by the number of items produced. Each tank costs $284.00 to produce

42. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150

43. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 Dimension A : # of spaces between holes = # holes – 1

44. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 Dimension A : # of spaces between holes = # holes – 1 # of spaces between holes = 7 – 1 = 6

45. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 Dimension A : # of spaces between holes = # holes – 1 # of spaces between holes = 7 – 1 = 6 Distance A = 20” x 6 = 120“ 120

46. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 To find dimension B… 120

47. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 To find dimension B, we will have to first find the distance between the first and last hole. 120

48. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 120

49. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 120

50. EXAMPLE #3 ( applications ): Two sets of holes are drilled in an aluminum plate in the figure below. Find in inches dimensions A and B A = _______ inches B = _______ inches 7 holes equally spaced 5 holes equally spaced 20 A B 30 40 150 120 20