course Mth 151
If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
018. `query 18
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `qquery 4.1.6 egyptian form of 23,145
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Your solution:
2*10,000=20,000
3*1000 = 3,000
1* 100 = 100
4*10 = 40
5*1 = 5
Egyptian Form =
2 pointing fingers
3 lotus flowers
1 scroll
4 heel bones
5 strokes
Confidence Assessment:
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Given Solution:
`a** You have 20,000, represented by two pointing fingers, plus 3,000, represented by three lotus flowers, plus 100, represented by 1 scroll, 40, represented by four heel bones, and 5, represented by 5 sticks. **
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `qquery 4.1.30 lll sssss hhhh tt + ll sss sss hh ttt ttt
Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the given sum.
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Your solution:
3 lotus flowers = 3000
5 scrolls = 500
4 heel bones = 40
2 strokes = 2
___________________
3542
2 lotus flowers = 2000
6 scrolls = 600
2 heel bones = 20
6 strokes = 6
____________________
2626
3542 + 2626 = 6168
Confidence Assessment:
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Given Solution:
`a** STUDENT SOLUTION USING THE WRONG METHODS:
Pointing finger is 10,000
lotus flower is 1000
scroll is 100
heel bone is 10
tally stick is 1
So the first number is 3500 + 40 + 2 = 2542, the second number is 2626. Adding up 3542 + 2626 we get 6168.
INSTRUCTOR COMMENT: This isn't how the Egyptians would have reasoned this problem out. They didn't have our decimal system, and you can't work the problem in our system unless they could do the same.
We can use digits to refer to small numbers, understanding that they would also have had names for these digits, but we use our system any further than that.
They would almost certainly have reasoned something like this:
You have a total of tt ttt ttt, which we represent as 8 tally sticks.
You have hhhh hh, which we represent as 6 heel bones.
You have sssss sss sss, which is the same as l s or 1 lotus flower to be included in the next step with the other lotus flowers, and one scroll.
You have lll ll in the original sum plus the l from the l ss you got in the previous step, for a total lll lll, which we see as six lotus flowers.
So the sum is lll lll ss hhhh hh tt ttt ttt.
6 lotus flowers represents 6 * 1,000 = 6,000 in our decimal system.
1 scroll represents 1 * 100 = 100 in our decimal system.
6 heel bones represents 6 * 10 = 60 in our decimal system.
8 tally sticks represents 8 * 1 = 8 in our decimal system.
The total is 6,000 + 100 + 60 + 8 = 6,168. **
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `qquery 4.1.30 ppp ll h ttt + pp l sssss hhhh hhhh tttt tttt
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Your solution:
3 pointing fingers = 30,000
2 lotus flowers = 2000
1 heel bone = 10
3 strokes = 3
______________________
32,013
2 pointing fingers = 20,000
1 lotus flower = 1000
5 scrolls = 500
8 heel bones = 80
8 strokes = 8
________________________
21,588
32,013 + 21,588 = 53,601
Confidence Assessment:
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Given Solution:
`aCOMMON ERROR AND INSTRUCTOR RESPONSE: The numbers are 32,013 and 21,588. When we add these numbers we get 63,601. This is ppp ppp lll sss sss t.
The Egyptians would have reasoned something like this:
You have 11 tally sticks, which will be represented by a heel bone and a tally stick.
You have nine heel bones in the sum, plus the one we get from the 10 tally sticks, so there are 10 heel bones. They will all be represented by a single scroll and no heel bones.
You have five scrolls, which in addition to the one that now represents the 10 heel bones gives you six scrolls.
There are three lotus flowers.
There are five pointing fingers.
So the sum is ppppp lll ssssss t.
This can all be summarized as follows:
ppp ll h ttt
+ pp l sssss hhhh hhhh tttt tttt
= ppp pp ll l sssss hhhh hhhh h ttt tttt tttt
= ppp pp ll l sssss hhhh hhhh hh t
= ppp pp ll l sssss s t
or ppppp lll ssssss t
which stands for 5,168. **
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Self-critique (if necessary):
How do you get 63,601? Isn’t 32,013+21,588=53,601?
That's correct.
Self-critique Rating:
Question: **** `q query 4.1.36 Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the product 36 * 81
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Your solution:
36*81=2916
3 heel bones = 30
6 strokes = 6
_______________
36
8 heel bones = 80
1 stroke = 1
_______________
81
36*81=2916
2 lotus flowers = 2000
9 scrolls = 900
1 heel bone = 10
6 strokes = 6
___________________
2916
Confidence Assessment:
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Given Solution:
`a** We use the Egyptian algorithm.
The first column will represent the numbers 1, 2, 4, 8 and 16. The second column will contain 81, 162, 324, 648 and 1296. Written out this looks like
1 81
2 162
4 324
8 648
16 1296
32 2592.
These numbers would of course have been written by the Egyptians using their notation. Doubling a number is done by doubling the number of tally sticks, heel bones, scrolls, etc., then regrouping if there are more than 10 in any group.
Keeping our numbers in the first column, but understanding that they would have used their own notation, they would have written their second column as follows:
1 hhhh hhhh t
2 s hhh hhh tt
4 sss hh tttt
8 sss sss hh hh tttt tttt
16 l ss hh hh hh hh h ttt ttt
32 ll ss ss s hhhh hhhh h tt
To make up the number 36 on the left we need to use the third and sixth rows (4 and 32).
This means that we will add the corresponding numbers sss hh tttt and ll ss ss s hhhh hhhh h tt, which will give us ll ss ss s sss s h tttt tt, standing for 2916. **
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Self-critique (if necessary):
Sometimes your directions are not complete and they don’t go by the book. In this problem if I went by the book it would be 33*81. Also your directions did not say anything about using the Egyptian Algorithm. This why sometimes I get confused and do the wrong thing because I don’t understand what you want.
I believe the problem in the text specifically said to use the Egyptian algorithm.
Self-critique Rating:
Question: **** `q4.1.36 Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the product 21 * 44.
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Your solution:
1 44
2 88
4 176
6 352
8 704
16 1408
1+4+16=21 44+176+1408
Confidence Assessment:
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Given Solution:
`a**The first column will represent the numbers 1, 2, 4, 8 and 16. The second column will contain 44, 88, 176, 352, and 704. Written out this looks like
1 44
2 88
4 176
8 352
16 704
These numbers would of course have been written by the Egyptians using their notation. Doubling a number is done by doubling the number of tally sticks, heel bones, scrolls, etc., then regrouping if there are more than 10 in any group.
Keeping our numbers in the first column, but understanding that they would have used their own notation, we would have
1 hhhh tttt
2 hhhh hhhh tttt tttt
4 hhhh hhhh hhhh hhhh tttt tttt tttt tttt OR s hhh hhh h ttt ttt
8 ss hhh hhh hhh hhh hh ttt ttt ttt ttt OR sss hhhh h tt
16 sss sss hhhh h hhhh h tt tt OR sss sss s tt tt.
To make up the number 21 on the left we need to use the first, third and fifth rows.
This means that we will add the corresponding numbers 44, 176, 704.
44 is represented by hhhh tttt
176 is represented by s hhh hhh h ttt ttt
}704 is represented by sss sss s tt tt.
This gives us a total of sss sss s s hhh hhh h hhhh tt tt ttt ttt tttt, which is regrouped as
sss sss s s s hh tttt.
This represents 924. **
Ok I am lost the book shows this differently than you do and I don’t understand either one of you.
"
You followed the algorithm correctly; except for an error in the first column of your table, which is easily corrected, and will result in the correct answer.
Your table was listed as
1 44
2 88
4 176
6 352
8 704
16 1408
6 doesn't belong in the first column. If you double 4 you get 8, not 6. The table should read
1 44
2 88
4 176
8 352
16 704
If you then add the 1, 4 and 16 rows your answer will agree with the given solution.