#$&* course Mth 151 4/5/2012 10:11PM 018. `query 18
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Given Solution: `a** You have 20,000, represented by two pointing fingers, plus 3,000, represented by three lotus flowers, plus 100, represented by 1 scroll, 40, represented by four heel bones, and 5, represented by 5 sticks. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `qquery 4.1.30 lll sssss hhhh tt + ll sss sss hh ttt ttt Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the given sum. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: By adding them together I got that there was 8 sticks, 6 heel bones, 11 scrolls, and 5 lotus flowers. 10 of the scrolls can be combined into a lotus flower, so I have 6 lotus flowers and 1 scroll. llllll = 6000, s = 100, hhhhhh = 60, and tttttttt = 8, all of that added together equals 6168. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `qquery 4.1.30 ppp ll h ttt + pp l sssss hhhh hhhh tttt tttt YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: That added together gives you, pppp p lll ssss s hhhh hhhh h tttt tttt ttt. Combining 10 tally sticks into a heel bone gave me 1 tally stick and 10 heel bones. Combining the all the heel bones gave me 6 scrolls and 0 heel bones. Which gave me pppp p lll ssss ss t, the 5 pointing fingers = 50000, 3 lotus flowers = 3000, 6 scrolls = 600, 0 heel bones = 0, 1 stick = 1, which added together equals 53,601 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): How did you get 5,168, the 5 pointing figures gives you 50,000, the 3 lotus flowers give you 3,000, the 6 scrolls gives you 600, and the tally marks gives you 1, so shouldn't the answer be 53,601. The answer in the back of the book is also 53,601 ------------------------------------------------ Self-critique Rating: 3
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* 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 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The column on the left will be 1, 2, 4, 8, 16, and 32, and the one on the right will be 81, 162, 324,648, 1296, 2592. 32 and 4 on the left column make up 36. 32 and 4 correspond to 2592 and 324 on the right column. 2592 + 324 = 2916. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK #*&! ********************************************* 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 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The column on the left will be 1, 2, 4, 8, 16, and 32, and the one on the right will be 81, 162, 324,648, 1296, 2592. 32 and 4 on the left column make up 36. 32 and 4 correspond to 2592 and 324 on the right column. 2592 + 324 = 2916. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK #*&!#*&!