document.write( "Question 832577: (2/5+3/8)-3/20\r
\n" ); document.write( "\n" ); document.write( "I'm having a hard time trying to solve this problem I keep getting the wrong answer \n" ); document.write( "

Algebra.Com's Answer #502095 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "To add or subtract fractions, you need to express them as equivalent fractions with the same denominator.
\n" ); document.write( " $\"2%2F5=2%2A8%2F%285%2A8%29=16%2F40\"$ , $\"3%2F8=3%2A5%2F%288%2A5%29=15%2F40\"$ and $\"3%2F20=3%2A2%2F%2820%2A2%29=6%2F40\"$
\n" ); document.write( "I chose $\"40\"$ as a common denominator to add $\"2%2F5\"$ and $\"3%2F8\"$ because it is a multiple of both denominators $\"%22%28+5+and+8+%29%22\"$ :
\n" ); document.write( " $\"5%2A8=40\"$ .
\n" ); document.write( "The fact that $\"40\"$ is also a multiple of $\"20\"$ , the denominator of $\"3%2F20\"$ was just a lucky coincidence.
\n" ); document.write( "Finally, when we get $\"15%2F40\"$ as a result we realize that $\"15\"$ and $\"40\"$ are both multiples of $\"5\"$ , and that
\n" ); document.write( " $\"5%2F8=5%2A5%2F%288%2A5%29=25%2F40\"$ .
\n" ); document.write( "Since $\"5%2F8=25%2F40\"$ , we express the fraction in the simpler $\"5%2F8\"$ way of writing it.
\n" ); document.write( "If $\"5\"$ and $\"8\"$ had any factor in common, I would simplify the fraction further, but $\"5\"$ and $\"8\"$ have no common factor.
\n" ); document.write( "
\n" ); document.write( "NOTE ON EQUIVALENT FRACTIONS:
\n" ); document.write( " $\"2%2F5\"$ of a pizza cut into 5 equal slices is 2 slices.
\n" ); document.write( "Each slice is $\"1%2F5\"$ of the pizza.
\n" ); document.write( "You could mark your $\"2%2F5\"$ portion of that pizza by sprinkling oregano on those 2 slices.
\n" ); document.write( "If each one of all 5 slices is split into 8 equal wedges, the pizza will be split into
\n" ); document.write( " $\"5%2A8=40\"$ very thin pizza wedges, all the same size.
\n" ); document.write( "Each one of those 40 thin slivers of pizza is $\"1%2F40\"$ of the pizza.
\n" ); document.write( "Your portion, which was $\"2%2F5\"$ of the pizza, is now made up of
\n" ); document.write( " $\"2%2A8=16\"$ of those thin slivers, so it is $\"16%2F40\"$ .
\n" ); document.write( "It may be harder to eat that way, but $\"2%2F5=16%2F40\"$ .
\n" ); document.write( "The denominator (the bottom number) got multiplied times 8, because each of the original slices was split into 8 equal slivers of pizza, and now there is a total of $\"5%2A8=40\"$ such slivers to the whole pizza.
\n" ); document.write( "At the same time, the numerator (the top number, and the number of pieces in your portion was also multiplied times 8.
\n" ); document.write( "Multiplying numerator and denominator times the same number, you get an equivalent fraction. It has the same value. It is the same number, just written in a different way. \n" ); document.write( "

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