Question

Express $\frac{168}{-294}$ as a rational number with denominator:
(i) 14
(ii) −7
(iii) −49
(iv) 1470

Answer 1

Rational number with denominator:

$$\begin{gathered} \left(\mathrm{i}\right)14\mathrm{as}\mathrm{denominator}:\frac{168/-21}{-294/-21}=\frac{-8}{14}(\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denomintor}\mathrm{by}-21) \\ \left(\mathrm{ii}\right)-7\mathrm{as}\mathrm{denominator}:\frac{168/42}{-294/42}=\frac{4}{-7}(\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denomintor}\mathrm{by}42) \\ \left(\mathrm{iii}\right)-49\mathrm{as}\mathrm{denominator}:\frac{168/6}{-294/6}=\frac{28}{-49}(\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denomintor}\mathrm{by}6) \\ \left(\mathrm{iv}\right)1470\mathrm{as}\mathrm{denominator}:\frac{168\times -5}{-294\times -5}=\frac{-840}{1470}(\mathrm{Multiplying}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denomintor}\mathrm{by}-5) \end{gathered}$$