Answer
$\dfrac{3}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the $LCD$ to convert the terms of the given expression, $
\dfrac{2}{3}+\dfrac{5}{6}
,$ to similar terms. Once expressed as similar terms, operate on the numerators and copy the common denominator.
$\bf{\text{Solution Details:}}$
The prime factorization of $
3
$ is $
3=3^1.$ The prime factorization of $
6
$ is $
6=2^1\cdot3^1.$ Getting each factor with the highest exponent, then the $
LCD=2^1\cdot3^1=6
.$ Converting the terms of the given expression to similar terms by using the $LCD$ results to
\begin{array}{l}\require{cancel}
\dfrac{2}{3}\cdot\dfrac{2}{2}+\dfrac{5}{6}
\\\\=
\dfrac{4}{6}+\dfrac{5}{6}
\\\\=
\dfrac{4+5}{6}
\\\\=
\dfrac{9}{6}
\\\\=
\dfrac{\cancel3(3)}{\cancel3(2)}
\\\\=
\dfrac{3}{2}
.\end{array}
