Question 215851
{{{((3/4) + (2/5))/((1/2) +(3/5))}}}


There are two main methods of simplifying this.  A lot of books call it "Method I" compared to "Method II."  Probably the best way to explain it here is called "Method I".  I call this the "un-stacking method."


The longer line means "DIVIDE", so just "un-stack the problem like this:


{{{((3/4) + (2/5))}}} DIVIDED BY {{{((1/2) +(3/5))}}}


Next, you have to simplify each fraction by finding a common denominator for each.  The LCD for the first fraction is 20.  The second is 10.  Write it like this:


{{{((3/4) + (2/5))}}} DIVIDED BY {{{((1/2) +(3/5))}}}

{{{((3/4)*(5/5) + (2/5)*(4/4))}}} DIVIDED BY {{{((1/2)*(5/5) +(3/5)*(2/2))}}}



{{{((15/20) + (8/20))}}} DIVIDED BY {{{((5/10) +(6/10))}}}

{{{(23/20) }}} DIVIDED BY {{{(11/10) }}}


Now, invert the second fraction and multiply:

{{{(23/20)*(10/11) }}}

  
Divide out the 10:


{{{(23/2)*(1/11) }}}
{{{23/22}}}


I have a pretty good page about complex fractions if you need to this with variables like x and y.  If you need to see this, then find my homepage by doing a Google search for my last name "Rapalje".  Look for the "MATH IN LIVING COLOR" page near the top of my Homepage.  Choose "Intermediate Algebra", and look in Chapter 2 for the topic "Complex Fractions."


R^2 

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus