 ## ← Adding Real Numbers Application

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Knowledge encountered:

Number line
Positive and Negative numbers

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Showing Revision 5 created 03/22/2012 by HopefulTypist.

1. At the beginning of the week,
2. Stewart's checking account had a balance
3. of negative fifteen dollars and eight cents.
4. On Monday morning he deposited a check
5. for four hundred twenty-six dollars and ninety cents.
6. On Tuesday morning he deposited another check
7. for [one] hundred dollars.
8. How much was in Stewart's checking account
9. after the second deposit, so after both of these deposits right over here?
10. So, he starts off with a negative balance,
11. so a negative balance means
12. that he's overdrawn his checking account.
13. He actually owes the bank money now.
14. Luckily, he's now going to put some money in his bank account,
15. so he'll actually have a positive balance in his checking account.
16. So, he starts off with negative fifteen dollars and eight cents,
17. and then to that, he adds
18. four hundred twenty-six dollars and ninety cents.
19. And then he adds another hundred dollars.
20. So, he started off with negative fifteen dollars and eight cents,
21. and then to that, he adds four hundred twenty-six dollars
22. and ninety cents and a hundred dollars.
23. So, that's five hundred and twenty-six dollars and ninety cents.
24. And so, how much is he going to have in his bank account?
25. He started, owing fifteen dollars and eight cents,
26. and then he's going to add
27. five hundred twenty-six dollars and ninety cents.
28. So, one way to visualize it,
29. is if you think about it on the number line,
30. and this is zero right over here.
31. He starts off at negative fifteen-point-zero-eight,
32. but then he's going to add
33. five hundred and twenty-six dollars [and ninety cents].
34. This is fifteen-point-zero-eight to the left,
35. that's how much he owes,
36. and to that, he's going to add
37. five hundred and twenty-six [dollars and ninety cents].
38. So, I'm not drawing this to scale,
39. but to that he's going to add
40. five hundred and twenty-six dollars and ninety cents.
41. So, the amount that he's going to be in the positive
42. is going to be
43. five hundred twenty-six dollars and ninety cents,
44. minus the fifteen-point-zero-eight.
45. And, so, essentially it's going to be this length right over here,
46. that's how much he's going to be in the positive,
47. That's going to be five hundred twenty-six dollars and ninety cents,
48. minus fifteen dollars and eight cents.
49. So, that's going to be--
50. and we can even just rewrite this
51. so that it actually looks exactly like that.
52. That's the exactly the same thing as
53. five hundred twenty-six dollars and ninety cents,
54. minus--
55. minus--
56. adding a negative is the same thing
57. as subtracting a positive--
58. minus fifteen-point-oh-eight.
59. --I will do this in another color--
60. Five hundred and twenty-six dollars and ninety cents,
61. minus fifteen dollars and eight cents.
62. Let's see, zero is less than eight,
63. let's make that a ten and borrow from this nine,
64. so that becomes an eight--
65. or I guess you could say, we are regrouping--
66. Everything up here is larger than everything there,
67. so ten minus eight is two,
68. eight minus zero is eight,
69. we have our decimal.
70. Six minus five is one.
71. Two minus one is one,
72. and then you have five minus nothing.
73. So, he is left
74. with five hundred eleven dollars and eighty-two cents,
75. after his second deposit.