Question

Express each of the following rational numbers in standard form:

(i) $\frac{-209}{247}$
(ii) $\frac{-46}{115}$
(iii) $\frac{84}{-147}$

Answer 1

$\begin{array}{l}\left(i\right)\frac{-209}{247}\\ \mathrm{H}.\mathrm{C}.\mathrm{F}.of209and247is19.\\ \begin{array}{l}\mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}19\\ \begin{array}{l}=\frac{-209÷19}{247÷19}=\frac{-11}{13}\\ \end{array}\end{array}\end{array}$


$$\begin{gathered} \begin{array}{l}\left(ii\right)\frac{-46}{115}\\ \begin{array}{l}\mathrm{H}.\mathrm{C}.\mathrm{F}.of46\mathrm{and}115\mathrm{is}23\\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}23\end{array}\end{array} \\ =\frac{-46÷23}{115÷23}=\frac{-2}{5} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\frac{84}{-147} \\ \mathrm{Converting}\mathrm{the}\mathrm{number}\mathrm{to}\mathrm{a}\mathrm{positive}\mathrm{denominator}: \\ \frac{84\times (-1)}{-147\times (-1)}=\frac{-84}{147} \\ \mathrm{H}.\mathrm{C}.\mathrm{F}.of84\mathrm{and}147is21 \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}21 \\ =\frac{-84÷\left(21\right)}{147÷\left(21\right)}=\frac{-4}{7} \end{gathered}$$