Small Base, Long DivisionDate: 10/06/2015 at 10:58:44 From: obinna Subject: with respect to division of numbers with bases other than te How can I divide 12343 by 24 in base five? I haven't tried it, it's just too confusing. Date: 10/06/2015 at 21:31:06 From: Doctor Peterson Subject: Re: with respect to division of numbers with bases other than te Hi, Obinna. Here is an example of division in base five using different numbers, so you can practice with your own: Divide 2431 by 32 in base five. First, I'll do something my son did when he was learning to divide, and which is very helpful in other bases: make a list of multiples of the divisor, to make it easy to find the appropriate quotient. This requires only repeatedly adding the divisor, all work being in base five. 32 32*1 + 32 ---- 114 32*2 + 32 ---- 201 32*3 + 32 ---- 233 32*4 + 32 ---- 320 32*10 (I didn't need that last addition, but did it as a check: the answer is clearly right, so I probably did all the additions in between correctly.) The resulting multiplication table is 1 2 3 4 +----------------- 32 |32 114 201 233 Now I can start the division: 4 ------- 32 ) 2431 <-- The biggest multiple less than 243 is 233 <-- 233, which is 4*32, so the quotient is 4. --- 10 <-- Subtract 233 from 243, leaving 10 Now I "bring down" the next digit, 1, and repeat the process: 41 ------- 32 ) 2431 233 --- 101 <-- The biggest multiple less than 101 is 32 <-- 32, which is 1*32, so the quotient is 1. --- 14 <-- Subtract 32 from 101, leaving 14 The quotient is 41 base five, and the remainder is 14 base five. To check the answer, we can convert to base ten. Our answer is a claim that 32 * 41 + 14 = 2431 (base five) Converting to base ten, this is 17 * 21 + 9 = 366 (base ten) This is correct! We could also check by multiplying in base five, if you prefer: 32 * 41 ---- 32 233 ---- 2412 + 14 ---- 2431 Again, the check passes. Now try your problem; if you have trouble, show me your work and I can help you check the steps. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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