Question 5.3.15: Using the Order of Operations Evaluate the expression using ......

Since division is performed before subtraction, we begin by performing the division. To divide by \frac{7}{9} , multiply by the reciprocal, \frac{9}{7}.

= \frac{13}{15} – \frac{14}{45} ÷ \frac{7}{9}

= \frac{13}{15} – \frac{14}{45} · \frac{9}{7}

= \frac{13}{15} – \frac{\cancel{14}^{2 · \cancel{7}}}{\cancel{45}_{5 · \cancel{9}}} · \frac{9}{7}     Write 14 as 2 · 7 and 45 as 5 · 9
and cross out common factors

= \frac{13}{15} – \frac{2}{5}

= \frac{13}{15} – \left ( \begin{matrix} \frac{2}{5} · \frac{3}{3} \end{matrix} \right )     Rewrite \frac{2}{5} with the LCD, 15.

\frac{13}{15} – \frac{6}{15} = \frac{7}{15}