document.write( "Question 1191598: What is 14203 base5 divided 12 base5? \n" ); document.write( "
Algebra.Com's Answer #823385 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "Unless you have a lot of experience with this kind of calculation, you probably want to start by making a table of the multiples of 12 in base 5. Then the division process is exactly the same as in base 10 -- you just have to do the calculations in base 5.
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document.write( "multiples of 12 in base 5:\r\n" );
document.write( " 12*1 = 12\r\n" );
document.write( " 12*2 = 12+12 = 24\r\n" );
document.write( " 12*3 = 24+12 = (36) = 41\r\n" );
document.write( " 12*4 = 41+12 = (53) = 103\r\n" );
document.write( " 12*5 = 103+12 = (115) = 120\r\n" );
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document.write( "Note it is useful to calculate 12*5 in base 5 to verify that the result is 120; it gives you confidence that you have calculated all the multiples of 12 correctly.\r\n" );
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document.write( "Now do the long division in base 5\r\n" );
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document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
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document.write( "Comparing the first digits \"14\" to the multiples of 12, we see that 14 is between 12 and 24; so the first digit of the answer is 1.\r\n" );
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document.write( "       1\r\n" );
document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
document.write( "      12\r\n" );
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document.write( "As in long division in base 10, subtract and \"bring down\" the next digit\r\n" );
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document.write( "       1\r\n" );
document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
document.write( "      12\r\n" );
document.write( "      ---\r\n" );
document.write( "       22\r\n" );
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document.write( "Again compare the \"22\" to the list of multiples of 12 to see that again these digits are between 12 and 24, so the next digit of the answer is also 1.  Again do the subtraction and bring down the next digit.\r\n" );
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document.write( "       11\r\n" );
document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
document.write( "      12\r\n" );
document.write( "      ---\r\n" );
document.write( "       22\r\n" );
document.write( "       12\r\n" );
document.write( "       ---\r\n" );
document.write( "       100\r\n" );
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document.write( "Repeat the process.  100 is between 41 and 103, so the next digit of the answer is 3.\r\n" );
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document.write( "       113\r\n" );
document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
document.write( "      12\r\n" );
document.write( "      ---\r\n" );
document.write( "       22\r\n" );
document.write( "       12\r\n" );
document.write( "       ---\r\n" );
document.write( "       100\r\n" );
document.write( "        41\r\n" );
document.write( "        ---\r\n" );
document.write( "         43\r\n" );
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document.write( "And to get the last digit in the quotient we again see that 43 is between 41 and 103, so the last digit in the quotient is another 3.\r\n" );
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document.write( "       1133\r\n" );
document.write( "    ---------\r\n" );
document.write( "  12) 14203\r\n" );
document.write( "      12\r\n" );
document.write( "      ---\r\n" );
document.write( "       22\r\n" );
document.write( "       12\r\n" );
document.write( "       ---\r\n" );
document.write( "       100\r\n" );
document.write( "        41\r\n" );
document.write( "        ---\r\n" );
document.write( "         43\r\n" );
document.write( "         41\r\n" );
document.write( "         --\r\n" );
document.write( "          2
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\n" ); document.write( "\n" ); document.write( "ANSWER: The quotient in base 5 is 1133; the remainder is 2.

\n" ); document.write( "We can, if we want, verify the answer by converting everything to base 10:

\n" ); document.write( "12 base 5 = 7 base 10
\n" ); document.write( "14203 base 5 = 1178 base 10
\n" ); document.write( "1133 base 5 = 168 base 10

\n" ); document.write( "1178/7 base 10 = 168 base 10
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