1. Place Value Identifying place value of a number is important.

2. Place Value Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

3. Place Value Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course. Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, The digits for each number will fall into one of these places. The last digit will always be in the ones place…

4. Place Value Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course. Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, The value of each place starting from the right ( ones place ) is 10 times larger.

5. Place Value Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course. Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each…

6. Place Value Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course. Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732

7. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

8. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148 Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

9. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148ones place Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

10. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148ones place 136,250 Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

11. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148ones place 136,250thousands place Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

12. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148ones place 136,250thousands place 123,456,789 Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

13. Place Value Billions Hundred Thousands Ten Thousands Thousands Hundred Millions Ten Millions Millions Hundreds Tens Ones,,, EXAMPLE : Find the place value for the RED number in each… 6,732tens place 148ones place 136,250thousands place 123,456,789ten millions place Identifying place value of a number is important. For our purpose, going up to the billions place will be sufficient for any applications that will follow during this course.

14. Addition and Subtraction Addition of whole numbers is easy but you need to keep your numbers lined up properly by place value.

15. Addition and Subtraction Addition of whole numbers is easy but you need to keep your numbers lined up properly by place value. For Example : Evaluate 1,234 + 581

16. Addition and Subtraction

17. Now add each column and carry if you need to…

18. Addition and Subtraction Now add each column and carry if you need to…

19. Addition and Subtraction Now add each column and carry if you need to…

20. Addition and Subtraction Now add each column and carry if you need to…

21. Addition and Subtraction Subtraction also requires you to keep the place values lined up. Set up your problem and then subtract, borrowing if needed.

22. Addition and Subtraction Subtraction also requires you to keep the place values lined up. Set up your problem and then subtract, borrowing if needed. I like to use notebook paper on its side to use its columns to line up the place values…

23. Addition and Subtraction

25. Now subtract beginning with the ones column and borrow if needed…

26. Addition and Subtraction Now subtract beginning with the ones column and borrow if needed…

27. Addition and Subtraction Now subtract beginning with the ones column and borrow if needed…

28. Addition and Subtraction Now subtract beginning with the ones column and borrow if needed…

29. Addition and Subtraction Now subtract beginning with the ones column and borrow if needed…

30. Application Problems To really have an applied math course, we need to see where the math concepts relate to the real world. So where possible, we will look at real world examples of where the math is being used.

31. Application Problems To really have an applied math course, we need to see where the math concepts relate to the real world. So where possible, we will look at real world examples of where the math is being used. So we will need to learn how to read basic blue prints…

32. Application Problems In the figure below, you can see how linear dimensions are represented. 20 in 4 in

33. Application Problems In the figure below, you can see how linear dimensions are represented. Sometimes the dimension is listed inside the two markers along with the arrows that define that linear distance… such is the case with the 20 in. measurement. 20 in 4 in

34. Application Problems In the figure below, you can see how linear dimensions are represented. Sometimes the dimension is listed inside the two markers along with the arrows that define that linear distance… such is the case with the 20 in. measurement. 20 in 4 in There are other cases where the arrows and dimension value are too big to fit into the space. So the dimension value will appear inside, and the arrows will appear outside and squeeze in towards the dimension’s value.

35. Application Problems Some figures will have holes shown. The holes will have the center marked with a plus sign, and lines extending from that center out a little beyond the edge of the circle.

36. Application Problems Some figures will have holes shown. The holes will have the center marked with a plus sign, and lines extending from that center out a little beyond the edge of the circle. Distance between holes will be shown as center to center. 14 cm

37. Application Problems Some figures will have holes shown. The holes will have the center marked with a plus sign, and lines extending from that center out a little beyond the edge of the circle. Distance between holes will be shown as center to center. Distance from an edge or from other parts of the figure will also be shown to center of given circles. 14 cm 50 cm

38. Application Problems Some figures will have holes shown that are equally spaced apart.

39. Application Problems Some figures will have holes shown that are equally spaced apart. A horizontal or vertical line will run through the centers to show their centers will all be on the same line.

40. Application Problems Some figures will have holes shown that are equally spaced apart. A horizontal or vertical line will run through the centers to show their centers will all be on the same line. There will also be a vertical or horizontal lines through each circle to show center.

41. Application Problems The number of holes will also be shown… 8 holes equally spaced apart

42. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure.

43. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 )

44. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 ) = 80

45. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 ) = 80 To Find B : Take the total length ( 100 ) – ( 20 ) – ( 50 )

46. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 ) = 80 To Find B : Take the total length ( 100 ) – ( 20 ) – ( 50 ) = 30

47. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 ) = 80 To Find B : Take the total length ( 100 ) – ( 20 ) – ( 50 ) = 30 To find C : Take the given height ( 35 ) – ( 16 )

48. APPLICATION PROBLEMS EXAMPLE : Find all missing dimensions in the figure. To find A : Take the total length ( 100 ) – ( 20 ) = 80 To Find B : Take the total length ( 100 ) – ( 20 ) – ( 50 ) = 30 To find C : Take the given height ( 35 ) – ( 16 ) = 19

49. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827

50. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

51. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

52. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

53. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

54. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

55. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To calculate how many parts each machine made subtract counter reading beginning of week from counter reading at the end of the week…

56. APPLICATION PROBLEMS EXAMPLE # 2 : Using the given table, find : a) how many parts are produced during the week for each machine ? b) what is the total weekly production ? Machine 1Machine 2Machine 3Machine 4Machine 5 Counter reading beginning of week 592643619588604 Counter reading end of the week 865766771713827 To get the weekly total add the column of parts made for the week…