Egyptian DivisionDate: 06/23/98 at 13:28:29 From: Anne Fogg Subject: Egyptian Division My fourth graders are studying ancient Egypt. We have tried working with Egyptian multiplication but haven't found any reference to division. What format did the ancient Egyptians use for dividing? Can you help? Date: 06/24/98 at 16:57:52 From: Doctor Mateo Subject: Re: Egyptian Division Hello Anne, Egyptian division is basically Egyptian multiplication in reverse. The divisor is repeatedly doubled to give the dividend. For example, 153 divided by 9. powers of two divisor and successive doubling (doubling) 2^0 = 1 9 2^1 = 2 18 2^2 = 4 36 2^3 = 8 72 2^4 = 16 144 2^5 = 32 288 288>153 so you can stop. Look for the combination of numbers that add up to 153 in the divisor column. This can be like a puzzle for the students and an excellent way to teach the problem-solving method known as guess and check. The combination that works here is 144 + 9 since 144 + 9 = 153. To determine the divisor, look at the corresponding column of powers of two. Here we have: 2^4 corresponding with 144 and 2^0 corresponding with 9. So the divisor is 2^4 + 2^0 = 16 + 1 = 17. The complication with Eqyptian division comes with remainders. For example, 17 divided by 3. Powers of two column divisor doubling column 2^0 = 1 3 2^1 = 2 6 2^2 = 4 12 2^3 = 8 24 24>17 so we can stop. Looking at the combinations of 3, 6, and 12 we see that 12 + 3 = 15 is the closest we can seem to get without going over 17. So what did the Eqyptians do to take care of the remainder? They found 2/3 of the divisor and then took one-half of that result. We choose 2/3 in this problem because 3 is the divisor. And since we know that 3/3 = 1, we can go ahead and determine the value associated with 1/3 too. When 3 is the divisor the possible remainders are 0/3, 1/3, and 2/3. So now we have: Powers of two column divisor doubling column 2^0 = 1 3 2^1 = 2 6 2^2 = 4 12 2/3 2 (2/3 of 3 = 2) 1/3 1 (1/2 of 2/3 of 3 = 1) So now in the divisor column what sums up to 17? 3 + 12 + 2 = 17 and this corresponds to what in the powers of two column. 2^0 + 2^2 + 2/3 = 1 + 4 + 2/3 = 5 2/3 If you are looking for resources on Eqyptian division I would consider checking out some books on the history of mathematics or methods of teaching elementary mathematics. Hope that this helps. Thank you for writing to Ask Dr. Math. - Doctor Mateo, The Math Forum http://mathforum.org/dr.math/ |
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