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 #761429 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "m/n < 1/5 and m+n=100 means

\n" ); document.write( " $\"m%2F%28100-m%29%3C1%2F5\"$
\n" ); document.write( " $\"5m+%3C+100-m\"$
\n" ); document.write( " $\"6m+%3C+100\"$
\n" ); document.write( " $\"m+%3C+100%2F6+=+50%2F3\"$

\n" ); document.write( "Since m is an integer, the maximum possible value for m is 16.

\n" ); document.write( "To maximize the value of m/n, with the requirement that m+n=100, m must be as large as possible. So the possible values we need to look at for m are 16, 15, 14, ....

\n" ); document.write( "If m is even, then n=100-m will also be even, and m/n will not be a reduced fraction.

\n" ); document.write( "If m is a multiple of 5, then n=100-m will also be a multiple of 5, and m/n will not be a reduced fraction.

\n" ); document.write( "So m can't be 16, 15, or 14. So

\n" ); document.write( "m=13 --> n = 87

\n" ); document.write( "The largest fraction that satisfies the conditions of the problem is

\n" ); document.write( "m/n = 13/87 \n" ); document.write( "

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