document.write( "Question 114218: The reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number? I am having such a hard time with this one I don't know why but I just can't get it!! \n" ); document.write( "

Algebra.Com's Answer #83291 by jgr45(31) $\"\"$ $\"About$

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The reciprocal of a number is what you multiply it by to get 1. So the reciprocal of 4 is $\"1%2F4\"$ because $\"1%2F4\"$ x 4 equals 1. Similarly, the reciprocal of 5 is $\"1%2F5\"$ because $\"1%2F5\"$ x 5 equals 1.\r
\n" ); document.write( "\n" ); document.write( "So this becomes an addition of fractions: $\"1%2F4\"$ + $\"1%2F5\"$ .\r
\n" ); document.write( "\n" ); document.write( "Here's a little shortcut I saw on educational television one day: Contrary to what we've been taught in school all these years, you do not need a common denominator to add fractions; there is a much easier way: Take the cross-products and add them and put that over the product of the denominators, and reduce if possible. For example, $\"3%2F8\"$ + $\"2%2F5\"$ = 3x5 + 8x2 over 8x5, or 15+16 over 40, or $\"31%2F40\"$ (no further reduction is possible). Try it and see for yourself; this is the same answer you will get if you want to labor through the common denominator process.\r
\n" ); document.write( "\n" ); document.write( "If the numerators are both 1, as in your problem, the shortcut is even easier because now you're multiplying by 1 in each cross-product. So the answer here is simply the sum of the denominators over product of the denominators, $\"9%2F20\"$ .\r
\n" ); document.write( "\n" ); document.write( "Now your problem is asking for the reciprocal of this number, $\"9%2F20\"$ . What number times $\"9%2F20\"$ = 1? Well, you simply turn the fraction upside down: $\"20%2F9\"$ , because $\"9%2F20\"$ x $\"20%2F9\"$ = $\"180%2F180\"$ which is 1. So your answer is $\"20%2F9\"$ , or 2 $\"2%2F9\"$ . :) \n" ); document.write( "

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