document.write( "Question 108069: 13/15 - 11/20 =
\n" ); document.write( "Help again please, just need to no how to do these again. My mind is not of any help need proffesionals... \n" ); document.write( "
Algebra.Com's Answer #78744 by solver91311(24713)\"\" \"About 
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\"13%2F15-11%2F20\" requires that you find a common denominator. It is usually most convenient to find the lowest common denominator.
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\n" ); document.write( "First begin with the prime factorization of 15, which is 3 * 5.
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\n" ); document.write( "Then find the prime factorization of 20, which is 2 * 2 * 5.
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\n" ); document.write( "Therefore, the lowest common denominator has two factors of 2, one factor of 3, and one factor of 5, i.e. 2 * 2 * 3 * 5 = 60.
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\n" ); document.write( "Now you can multiply each of your fractions by 1 in the form of some \"a%2Fa\" where a = 60 divided by the denominator of the fraction.
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\n" ); document.write( "\"60%2F15=4\" so multiply the first fraction times \"4%2F4\":
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\n" ); document.write( "\"%2813%2F15%29%284%2F4%29=52%2F60\"
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\n" ); document.write( "Similarly, \"60%2F20=3\", so \"%28-11%2F20%29%283%2F3%29=-33%2F60\"
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\n" ); document.write( "Now your problem reads:
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\n" ); document.write( "\"52%2F60-33%2F60\"
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\n" ); document.write( "Since the denominators are now equal, you can add the numerators directly to get the requested sum:
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\n" ); document.write( "\"19%2F60\"
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\n" ); document.write( "Just to show the convenience of finding the lowest common denominator, if you had just multiplied the two denominators together to get a convenient common denominator that wasn't necessarily the lowest, in this case 300, you would have had the following result:\r
\n" ); document.write( "\n" ); document.write( "\"260%2F300-165%2F300=95%2F300\", and \"95%2F300\" is a rather messy fraction to have to reduce to lowest terms. I'll leave it as an exercise for you to prove that \"95%2F300=19%2F60\".
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