document.write( "Question 1161439: 322base5รท4base5
\n" ); document.write( "Figure the problem using base 5blocks.
\n" ); document.write( "Figure the problem using standard algorithm.
\n" ); document.write( "Figure the problem using repeated subtraction. \n" ); document.write( "
Algebra.Com's Answer #784997 by greenestamps(13327)\"\" \"About 
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\n" ); document.write( "(1) I don't know what \"base 5 blocks\" are....

\n" ); document.write( "(2) To divide using long division, it is helpful to have a multiplication table for 4 in base 5:

\n" ); document.write( "1*4 = 4 (base 10) = 4 (base 5)
\n" ); document.write( "2*4 = 8 = 13 (base 5)
\n" ); document.write( "3*4 = 12 = 22 (base 5)
\n" ); document.write( "4*4 = 16 = 31 (base 5)

\n" ); document.write( "Then in the subtraction part of the algorithm, you of course need to do the subtraction in base 5.
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document.write( "          4 1 remainder 3\r\n" );
document.write( "      --------\r\n" );
document.write( "    4 ) 3 2 2\r\n" );
document.write( "        3 1      [4*4 = 31]\r\n" );
document.write( "       ------\r\n" );
document.write( "          1 2    [subtract; bring down the next digit]\r\n" );
document.write( "            4    [4*1 = 4]\r\n" );
document.write( "          ---\r\n" );
document.write( "            3    [subtract to get the remainder]

\n" ); document.write( "(3) Solving using repeated subtraction is straightforward, but gives us a lot of practice in base 5 arithmetic....
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document.write( "1  322-4 = 313\r\n" );
document.write( "2  313-4 = 304\r\n" );
document.write( "3  304-4 = 300\r\n" );
document.write( "4  300-4 = 241\r\n" );
document.write( "5  241-4 = 232\r\n" );
document.write( "6  232-4 = 223\r\n" );
document.write( "7  223-4 = 214\r\n" );
document.write( "8  214-4 = 210\r\n" );
document.write( "9  210-4 = 201\r\n" );
document.write( "10 201-4 = 142\r\n" );
document.write( "11 142-4 = 133\r\n" );
document.write( "12 133-4 = 124\r\n" );
document.write( "13 124-4 = 120\r\n" );
document.write( "14 120-4 = 111\r\n" );
document.write( "15 111-4 = 102\r\n" );
document.write( "16 102-4 =  43\r\n" );
document.write( "17  43-4 =  34\r\n" );
document.write( "18  34-4 =  30\r\n" );
document.write( "19  30-4 =  21\r\n" );
document.write( "20  21-4 =  12\r\n" );
document.write( "21  12-4 =   3

\n" ); document.write( "We subtracted 4 21 times, which is 41 in base 5; and we were left with a remainder of 3. So again we got the result 322 divided by 4 in base 5 = 41 remainder 3.

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