Date: Sun, 15 Nov 1998 20:27:51 -0800 Sender: sara To: QandQ@MathCentral.uregina.ca Subject: middle 6-9 Hello! I am wondering why 16 and multiples of 16 do not work in the ancient duplation method of multiplication used by the Egyptians. I discovered the method in the Journeys math text gr 7 level. Just curious. Am I doing something wrong?? thanks
Sara
Dear Sara
2xa = 2x1a = 2a, 4xa = 2x2a = 4a, 8xa = 2x4a = 8a, 16xa = 2x8a = 16a.
At this point you have the answer to 16xa and need to go no further. But if you say that you want to use the technique shown on page 45 of Journeys in Mathematics 7, LeSage et al, Prentice Hall Ginn then you could could combine: 8xa, 4xa, 2xa, 1xa and 1xa or 8xa, 4xa, 2xa and 2xa or etc. In fact what you have discovered is that, when you are multiplying by powers of 2, the answer appears directly but that you can also obtain the answer by combining all of the answers from the previous powers of 2 and then adding again the 1st answer obtained by multiplying the number by 1. Write the right side of the previous expression as Multiply both sides by 2 to get Subtracting the previous two equations gives or Jack is one of the authors of JIM 7 and wants thank you for this insight. Another way to look at what is going on with the duplation method of multiplication is to notice that the doubling procedure expresses the multiplyer in base 2. So if you want to find, say 19a, again by the doubling method write
2xa = 2x1a = 2a, 4xa = 2x2a = 4a, 8xa = 2x4a = 8a, 16xa = 2x8a = 16a.
Cheers, To return to the previous page use your browser's back button. |