document.write( "Question 1140817: the reduced fraction m/n is less than 1/5 and m+n=100 find the greatest possible such fraction \n" ); document.write( "

Algebra.Com's Answer #761413 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The answer $\"m%2Fn\"$ = $\"16%2F84\"$ which tutor @ankor found, is not the solution to the problem, \r
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\n" ); document.write( "\n" ); document.write( " since the fraction $\"16%2F84\"$ is not reduced. I came to bring the correct answer and solution.\r
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document.write( "m + n = 100   ====>  n = 100-m.\r\n" );
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document.write( "So the inequality   <    takes the form\r\n" );
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document.write( "     < \r\n" );
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document.write( "    5m < 100 - m\r\n" );
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document.write( "    6m < 100\r\n" );
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document.write( "    m  <  = 16.66...\r\n" );
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document.write( "    m <= 16.\r\n" );
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document.write( "Now we should consider all the fractions    with  0 <= m <= 16 and select maximal of that which IS REDUCED.\r\n" );
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document.write( "I did it using EXCEL.  See the table below.\r\n" );
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document.write( "      T   A   B   L   E   \r\n" );
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document.write( "m     100-m      -reduced or not    Value of \r\n" );
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document.write( "16	84	    No	\r\n" );
document.write( "15	85	    No	\r\n" );
document.write( "14	86	    No	\r\n" );
document.write( "13	87	    Yes                          0.149425287   <<<---===  The maximum value :  the solution and the answer\r\n" );
document.write( "12	88	    No	 \r\n" );
document.write( "11	89	    Yes	                         0.123595506\r\n" );
document.write( "10	90	    No	 \r\n" );
document.write( "9	91	    Yes	                         0.098901099\r\n" );
document.write( "8	92	    No	 \r\n" );
document.write( "7	93	    Yes	                         0.075268817\r\n" );
document.write( "6	94	    No	\r\n" );
document.write( "5	95	    No	\r\n" );
document.write( "4	96	    No	\r\n" );
document.write( "3	97	    Yes	                         0.030927835\r\n" );
document.write( "2	98	    No	\r\n" );
document.write( "1	99	    Yes	                         0.01010101\r\n" );
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document.write( "ANSWER.  The greatest possible such fraction is   = 0.149425287.\r\n" );
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