Basic Math and a Spreadsheet
We have been studying basic properties of Algebra and using them to simplify expressions. You are probably wondering how this simple stuff can be relevant in the real world.
I used to work for a bookkeeping and tax service. We used a modification of the Class Life ADR system and prorated the depreciation for the year of acquisition based upon the number of months the item was in service. Below is a portion of the manual form:
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(a) Full Year Depreciation |
(b) Months In Service |
( c) Multiply (a) by (b) |
(d) Divide ( c) by 12 |
(e) Depreciation This Year (Round) |
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Totals |
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We wanted to computerize this form, but the initial tests were disappointingly slow. My revision of the form looked like this:
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(a) Full Year Depreciation |
(b) Months In Service |
( c) Multiply (a) by (b) |
(d) Divide ( c) by 12 |
(e) Depreciation This Year (Round) |
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Totals |
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Why? Let A, B, and C represent the full year depreciation for our three items and D, E, and F the number of months each was in service, respectively.
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(a) Full Year Depreciation |
(b) Months In Service |
( c) Multiply (a) by (b) |
(d) Divide ( c) by 12 |
(e) Depreciation This Year (Round) |
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A |
D |
AD |
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B |
E |
BE |
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C |
F |
CF |
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Totals |
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The total of column ( c) would be
AD + BE + CF.
Column (d) would contain
(AD + BE + CF)/12.
[3 multiplications, 2 additions, 1 division]
In the old form, the total of column (D) was
AD/12 + BE/12 + CF/12.
[3 multiplications, 2 additions, 3 divisions]
We did not need both of these quantities. We only needed one; the other acted as a self-check. The only quantity really used was the total of column (e).
We saved 2 divisions with just three items. Division is one of the most expensive operations in terms of time. Notice that we have not counted the number of “round-offs” and additions that were saved by not having column (e). Nor have we counted the reduced printing time!
Did you recognize the Distributive Property, A(B +C) = AB + AC ?
(AD + BE + CF)/12 = AD/12 + BE/12 + CF/12
Have you ever built a large spreadsheet? Were you frustrated by how long it took to recalculate after one little change? Could some thought about the underlying mathematics have made it faster?