91Ó°ÊÓ

Consider the expression.

$\frac{7}{10}-w$

Substitute $\frac{1}{2}$for $w$into the given expression.

$\frac{7}{10}-w=\frac{7}{10}-\frac{1}{2}$

Conclude that the fractions have different denominators.

So, find the least common denominator of $10$and $2$.

$\begin{array}{rcl}10& =& 2·5\\ 2& =& 2·1\\ & ⇒& LCM=2·5\\ & ⇒& LCM=10\end{array}$

Rewrite as equivalent fractions with the least common denominator, $10$.

$\frac{7}{10}-w=\frac{7}{10}·\frac{1}{1}-\frac{1}{2}·\frac{5}{5}$

Simplify.

$\frac{7}{10}-w=\frac{7}{10}-\frac{5}{10}$

Subtract the fractions to simplify the expression.

$\begin{array}{rcl}\frac{7}{10}-w& =& \frac{7-5}{10}\\ & =& \frac{2}{10}\\ & =& \frac{1}{5}\end{array}$

Thus, the value of the given expression when $w=\begin{array}{rcl}& & \frac{1}{2}\end{array}$is $\begin{array}{rcl}& & \frac{1}{5}\end{array}$.

Substitute $-\frac{1}{2}$for $x$into the given expression.

$\frac{7}{10}-w=\frac{7}{10}-\left(-\frac{1}{2}\right)$

Conclude that the fractions have different denominators.

So, find the least common denominator of $10$and $2$.

The least common denominator is $10$.

Rewrite as equivalent fractions with the least common denominator, $10$.

$\frac{7}{10}-w=\frac{7}{10}·\frac{1}{1}-\left(-\frac{1}{2}·\frac{5}{5}\right)$

Simplify.

$\frac{7}{10}-w=\frac{7}{10}-\left(-\frac{5}{10}\right)$

Subtract the fractions to simplify the expression.

$\begin{array}{rcl}\frac{7}{10}-w& =& \frac{7-(-5)}{10}\\ & =& \frac{12}{10}\\ & =& \frac{6}{5}\end{array}$

Thus, the value of the given expression when $w=-\begin{array}{rcl}& & \frac{1}{2}\end{array}$is $\begin{array}{rcl}& & \frac{6}{5}\end{array}$.