Question 108069
{{{13/15-11/20}}} requires that you find a common denominator.  It is usually most convenient to find the lowest common denominator.
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First begin with the prime factorization of 15, which is 3 * 5.
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Then find the prime factorization of 20, which is 2 * 2 * 5.
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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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Now you can multiply each of your fractions by 1 in the form of some {{{a/a}}} where a = 60 divided by the denominator of the fraction.
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{{{60/15=4}}} so multiply the first fraction times {{{4/4}}}:
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{{{(13/15)(4/4)=52/60}}}
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Similarly, {{{60/20=3}}}, so {{{(-11/20)(3/3)=-33/60}}}
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Now your problem reads:
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{{{52/60-33/60}}}
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Since the denominators are now equal, you can add the numerators directly to get the requested sum:
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{{{19/60}}}
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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:

{{{260/300-165/300=95/300}}}, and {{{95/300}}} is a rather messy fraction to have to reduce to lowest terms.  I'll leave it as an exercise for you to prove that {{{95/300=19/60}}}.