How do you simplify #\frac { 11x ^ { 2} } { 33x } + \frac { 5x ^ { 2} } { 15x }#?

2 Answers
sankarankalyanam
Nov 10, 2017

#= (2x)/3#

Explanation:

#((11x^2)/(33x)) + ((5x^2)/(15x))#

#= ((11*x*x)/(11*3*x)) + ((5*x*x)/(5*3*x))#

#= ((cancel(11*x)*x)/ (cancel(11*x)*3)) + ((cancel(5*x)*x) / (cancel(5*x)*3))#

#=(x/3) + (x/3)#
#= (2x)/3#

Ms. Worth
Nov 10, 2017

#(2x)/3#

Explanation:

1) First cancel any factors that are in common in the numerators and in their own denominators.
Because this is an addition problem (not a multiplication problem), you can cancel common factors only within the same fraction.

For the first term
#(11 x^2)/(33x) #

#(11)/(33)# reduces to #(1)/(3)#

#(x^2) / (x) # reduces to #(x)/(1)#

So the first term simplifies to
#(1)/(3)# × #(x)/(1)#

#(x)/(3)#
................................

For the second term
#(5x^2)/(15x)#

#(5)/(15)# reduces to #(1)/(3)#

#(x^2)/(x)# reduces to #(x)/(1)#

So the second term simplifies to
#(1)/(3)# × #(x)/(1)#

#(x)/(3)#
..................

Now the problem has been simplified to
#(x)/(3)# + #(x)/(3)#

The fractions have a common denominator, so you can just add.
Add the numerators and keep the common denominator.
#(x + x) / (3) #

#(2x)/3#

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