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

2 Answers
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

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