document.write( "Question 996758: Insert 25 rational number between 1/2and5/1
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Algebra.Com's Answer #615077 by MathLover1(20850) $\"\"$ $\"About$

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recall:
\n" ); document.write( "Rational Numbers - any number that is either an integer \" $\"a\"$ \" or is expressible as the ratio of two integers, $\"a%2Fb\"$ . The numerator, \" $\"a\"$ \", may be any whole number, and the denominator, \" $\"b\"$ \", may be any positive whole number greater than zero. If the denominator happens to be unity, $\"+b+=+1\"$ , the ratio is an integer. If \" $\"b\"$ \" is other than $\"1\"$ , $\"+a%2Fb+\"$ is a fraction.\r
\n" ); document.write( "\n" ); document.write( "to find $\"25\"$ rational numbers between $\"1%2F2\"$ and $\"5%2F1=5\"$ ,solve inequality\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F2%3Cx%3C5\"$ you can start with fractions, or you can pick numbers like \r
\n" ); document.write( "\n" ); document.write( " $\"0.5%3Cx%3C5\"$ and write them all as fractions; it’s easier way to find them\r
\n" ); document.write( "\n" ); document.write( "start with first number greater than $\"0.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0.6%3Cx%3C5\"$ => $\"6%2F10%3Cx%3C5\"$ => $\"3%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"0.7%3Cx%3C5\"$ => $\"7%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"0.8%3Cx%3C5\"$ => $\"8%2F10%3Cx%3C5\"$ => $\"4%2F5%3Cx%3C5+\"$
\n" ); document.write( " $\"0.9%3Cx%3C5\"$ => $\"9%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"1%3Cx%3C5\"$ => $\"1%2F1%3Cx%3C5\"$
\n" ); document.write( " $\"1.1%3Cx%3C5\"$ => $\"11%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"1.2%3Cx%3C5\"$ => $\"12%2F10%3Cx%3C5\"$ => $\"6%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"1.3%3Cx%3C5\"$ => $\"13%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"1.4%3Cx%3C5\"$ => $\"14%2F10%3Cx%3C5\"$ => $\"7%2F5%3Cx%3C5+\"$
\n" ); document.write( " $\"1.5%3Cx%3C5\"$ => $\"15%2F10%3Cx%3C5\"$ => $\"3%2F5%3Cx%3C5+\"$
\n" ); document.write( " $\"1.6%3Cx%3C5\"$ => $\"16%2F10%3Cx%3C5\"$ => $\"8%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"1.7%3Cx%3C5\"$ => $\"17%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"1.8%3Cx%3C5\"$ => $\"18%2F10%3Cx%3C5\"$ => $\"9%2F5%3Cx%3C5+\"$
\n" ); document.write( " $\"1.9%3Cx%3C5\"$ => $\"19%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"2%3Cx%3C5\"$ => $\"2%2F1%3Cx%3C5\"$
\n" ); document.write( " $\"2.1%3Cx%3C5\"$ => $\"21%2F10%3Cx%3C5+\"$
\n" ); document.write( " $\"2.2%3Cx%3C5\"$ => $\"22%2F10%3Cx%3C5\"$ => $\"11%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"2.3%3Cx%3C5\"$ => $\"23%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"2.4%3Cx%3C5\"$ => $\"24%2F10%3Cx%3C5\"$ => $\"12%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"2.5%3Cx%3C5\"$ => $\"25%2F10%3Cx%3C5\"$ => $\"5%2F2%3Cx%3C5\"$
\n" ); document.write( " $\"2.6%3Cx%3C5\"$ => $\"26%2F10%3Cx%3C5\"$ => $\"13%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"2.7%3Cx%3C5\"$ => $\"27%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"2.8%3Cx%3C5\"$ => $\"28%2F10%3Cx%3C5\"$ => $\"24%2F5%3Cx%3C5\"$
\n" ); document.write( " $\"2.9%3Cx%3C5\"$ => $\"29%2F10%3Cx%3C5\"$
\n" ); document.write( " $\"3%3Cx%3C5\"$ => $\"3%2F1%3Cx%3C5\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your numbers are:\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F2\"$ < $\"3%2F5\"$ , $\"7%2F10\"$ , $\"4%2F5\"$ , $\"9%2F10\"$ , $\"1%2F1\"$ , $\"11%2F10\"$ , $\"6%2F5\"$ , $\"13%2F10\"$ , $\"7%2F5\"$ , $\"3%2F5\"$ , $\"8%2F5\"$ , $\"17%2F10\"$ , $\"9%2F5\"$ , $\"19%2F10\"$ , $\"2%2F1\"$ , $\"21%2F10\"$ , $\"11%2F5\"$ , $\"23%2F10\"$ , $\"12%2F5\"$ , $\"5%2F2\"$ , $\"13%2F5\"$ , $\"27%2F10\"$ , $\"24%2F5\"$ , $\"29%2F10\"$ , $\"3%2F1\"$ < $\"5%2F1\"$ \r
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