91Ó°ÊÓ

Consider the expression.

$x+\left(-\frac{5}{6}\right)$

Substitute $\frac{1}{3}$for $x$into the given expression.

$x+\left(-\frac{5}{6}\right)=\frac{1}{3}+\left(-\frac{5}{6}\right)$

Conclude that the fractions have different denominators.

So, find the least common denominator of $3$and $6$.

$\begin{array}{rcl}3& =& 1·3\\ 6& =& 2·3\\ & ⇒& LCM=2·3\\ & ⇒& LCM=6\end{array}$

Rewrite as equivalent fractions with the least common denominator, $6$.

localid="1647943000034" $\begin{array}{rcl}x+\left(-\frac{5}{6}\right)& =& \frac{1}{3}·\frac{2}{2}+\left(-\frac{5}{6}\right)·\frac{1}{1}\end{array}$

Simplify.

localid="1647943004312" $\begin{array}{rcl}x+\left(-\frac{5}{6}\right)& =& \frac{2}{6}+\left(-\frac{5}{6}\right)\end{array}$

Add the fractions to simplify the expression.

localid="1647943743407" $\begin{array}{rcl}x+\left(-\frac{5}{6}\right)& =& \frac{2+(-5)}{6}\\ & =& \frac{-3}{6}\\ & =& -\frac{1}{2}\end{array}$

Thus, the value of the given expression when $x=\frac{1}{3}$is $-\frac{1}{2}$.

Substitute $-\frac{1}{6}$for $x$into the given expression.

$\begin{array}{rcl}x+\left(-\frac{5}{6}\right)& =& -\frac{1}{6}+\left(-\frac{5}{6}\right)\end{array}$

Conclude that the fractions have the same denominators.

Therefore, add the fractions to simplify the expression.

localid="1647943794533" $\begin{array}{rcl}x+\left(-\frac{5}{6}\right)& =& \frac{-1+(-5)}{6}\\ & =& \frac{-6}{6}\\ & =& -1\end{array}$

Hence, the value of the expression when $x=-\frac{1}{6}$is$-1$.