document.write( "Question 148905: Show the difference between a four-digit number and its reverse is divisible by 9 \n" ); document.write( "

Algebra.Com's Answer #109219 by Edwin McCravy(20056) $\"\"$ $\"About$

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Show the difference between a four-digit number and its reverse is divisible by 9\r
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document.write( "Suppose the number is \"ABCD\".\r\n" );
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document.write( "Then the value of the number is \r\n" );
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document.write( "1000A + 100B + 10C + D\r\n" );
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document.write( "and its reverse is \"DCBA\" with value\r\n" );
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document.write( "1000D + 100C + 10B + A\r\n" );
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document.write( "Now suppose \"ABCD\" is larger than \"DCBA\", then if we subtract them,\r\n" );
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document.write( "(1000A + 100B + 10C + D) - (1000D + 100C + 10B + A)\r\n" );
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document.write( "Remove the parentheses:\r\n" );
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document.write( "1000A + 100B + 10C + D - 1000D - 100C - 10B - A\r\n" );
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document.write( "999A + 90B - 90C - 999D\r\n" );
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document.write( "Factor out 9\r\n" );
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document.write( "9(111A + 10B - 10C - 111D)\r\n" );
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document.write( "This is a multiple of 9.\r\n" );
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document.write( "If \"DCBA\" is larger than \"ABCD\" we'll end up with\r\n" );
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document.write( "9(111D + 10C - 10B - 111A) \r\n" );
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document.write( "This is also a multiple of 9.\r\n" );
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document.write( "Edwin

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