Question

# Express each of the following rational numbers in standard form: (i) $\frac{-209}{247}$ (ii) $\frac{-46}{115}$ (iii) $\frac{84}{-147}$

Open in App
Solution

## $\begin{array}{l}\left(i\right)\frac{-209}{247}\\ \mathrm{H}.\mathrm{C}.\mathrm{F}.of209and247is19.\\ \begin{array}{l}\mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}19\\ \begin{array}{l}=\frac{-209÷19}{247÷19}=\frac{-11}{13}\\ \end{array}\end{array}\end{array}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$ $\begin{array}{l}\left(ii\right)\frac{-46}{115}\\ \begin{array}{l}\mathrm{H}.\mathrm{C}.\mathrm{F}.of46\mathrm{and}115\mathrm{is}23\\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}23\end{array}\end{array}\phantom{\rule{0ex}{0ex}}=\frac{-46÷23}{115÷23}=\frac{-2}{5}$ $\left(\mathrm{iii}\right)\frac{84}{-147}\phantom{\rule{0ex}{0ex}}\mathrm{Converting}\mathrm{the}\mathrm{number}\mathrm{to}\mathrm{a}\mathrm{positive}\mathrm{denominator}:\phantom{\rule{0ex}{0ex}}\frac{84×\left(-1\right)}{-147×\left(-1\right)}=\frac{-84}{147}\phantom{\rule{0ex}{0ex}}\mathrm{H}.\mathrm{C}.\mathrm{F}.of84\mathrm{and}147is21\phantom{\rule{0ex}{0ex}}\mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}21\phantom{\rule{0ex}{0ex}}=\frac{-84÷\left(21\right)}{147÷\left(21\right)}=\frac{-4}{7}$

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
Rational numbers in standard form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...