Question

Express each of the following rational numbers to the lowest form:
(i) $\frac{4}{22}$
(ii) $\frac{-36}{180}$
(iii) $\frac{132}{-428}$
(iv) $\frac{-32}{-56}$

Answer 1

Lowest form of:
$$\begin{gathered} \left(i\right)\frac{4}{22}\mathrm{is}: \\ 4=2\times 2 \\ 22=2\times 11 \\ \mathrm{HCF}\mathrm{of}4\mathrm{and}22\mathrm{is}2. \\ \text{D}\mathrm{ividing}\mathrm{the}\mathrm{fraction}\mathrm{by}2,\mathrm{we}\mathrm{get}\frac{2}{11}. \\ \left(\mathrm{ii}\right)\frac{-36}{180}\mathrm{is}: \\ 36=3\times 3\times 2\times 2 \\ 180=5\times 3\times 3\times 2\times 2 \\ \mathrm{HCF}\mathrm{of}36\mathrm{and}180\mathrm{is}36. \\ \text{D}\mathrm{ividing}\mathrm{the}\mathrm{fraction}\mathrm{by}36,\mathrm{we}\mathrm{get}\frac{-1}{5} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)\frac{132}{-428}\mathrm{is}: \\ 132=2\times 3\times 2\times 11 \\ 428=2\times 2\times 107 \\ \mathrm{HCF}\mathrm{of}132\mathrm{and}428\mathrm{is}4. \\ \text{D}\mathrm{ividing}\mathrm{the}\mathrm{fraction}\mathrm{by}4,\mathrm{we}\mathrm{get}\frac{33}{-107} \\ \left(\mathrm{iv}\right)\frac{-32}{-56}\mathrm{is}: \\ 32=2\times 2\times 2\times 2\times 2 \\ 56=2\times 2\times 2\times 7 \\ \mathrm{HCF}\mathrm{of}32\mathrm{and}56\mathrm{is}8. \\ \text{D}\mathrm{ividing}\mathrm{the}\mathrm{fraction}\mathrm{by}8,\mathrm{we}\mathrm{get}\frac{4}{7} \end{gathered}$$