Question

$\begin{array}{l}\text{Inthefollowingexercise,evaluate.}\\ \frac{5}{12}-w\text{When}\\ ⓐw=\frac{1}{4}ⓑw=-\frac{1}{4}\end{array}$

Short answer

$\begin{array}{l}\text{Theresultofevaluatingtheexpressionis}\\ a)\frac{1}{6}\\ b)\frac{2}{3}\end{array}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionis}\\ \frac{5}{12}-w\\ \text{Wewillevaluatetheexpressionforeachvalueof}w.\end{array}$

Step 2. Substitute the value of w from part (a)

$\begin{array}{l}\text{At}w=\frac{1}{4},\text{Wehave}\\ \Rightarrow \frac{5}{12}-\left(\frac{1}{4}\right)\\ =\frac{5}{12}-\frac{1}{4}\\ =\frac{5\times 4-1\times 12}{12\times 4}\\ =\frac{20-12}{48}\\ =\frac{8}{48}\\ =\frac{\cancel{8}}{6\times \cancel{8}}\\ =\frac{1}{6}\end{array}$

Step 3. Substitute the value of w from part (b) 

$\begin{array}{l}\text{At}w=-\frac{1}{4},\text{Wehave}\\ \Rightarrow \frac{5}{12}-\left(-\frac{1}{4}\right)\\ =\frac{5}{12}+\frac{1}{4}\\ =\frac{5\times 4+1\times 12}{12\times 4}\\ =\frac{20+12}{48}\\ =\frac{32}{48}\\ =\frac{2\times \cancel{16}}{3\times \cancel{16}}\\ =\frac{2}{3}\end{array}$