Question

Add:

(i) $\frac{3}{4}\mathrm{and}\frac{5}{6}$
(ii) $\frac{7}{10}\mathrm{and}\frac{2}{15}$
(iii) $\frac{8}{13}\mathrm{and}\frac{2}{3}$
(iv) $\frac{4}{5}\mathrm{and}\frac{7}{15}$

Answer 1

(i)

$$\begin{gathered} \frac{3}{4}+\frac{5}{6} \\ \mathrm{LCM}\mathrm{of}4\&6\mathrm{is}12,\mathrm{so}\mathrm{we}\mathrm{will}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}12. \\ =\frac{3\times 3}{4\times 3}+\frac{5\times 2}{6\times 2} \\ =\frac{9}{12}+\frac{10}{12} \\ =\frac{9+10}{12}=\frac{19}{12} \end{gathered}$$

(ii)

$$\begin{gathered} \frac{7}{10}+\frac{2}{15} \\ \mathrm{LCM}\mathrm{of}10\&15\mathrm{is}30,\mathrm{so}\mathrm{we}\mathrm{will}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}30. \\ =\frac{7\times 3}{10\times 3}+\frac{2\times 2}{15\times 2}=\frac{21}{30}+\frac{4}{30} \\ =\frac{21+4}{30} \\ =\frac{25}{30} \end{gathered}$$

(iii)

$$\begin{gathered} \frac{8}{13}+\frac{2}{3} \\ \mathrm{LCM}\mathrm{of}13\&3\mathrm{is}39,\mathrm{so}\mathrm{we}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}39. \\ =\frac{8\times 3}{13\times 3}+\frac{2\times 13}{3\times 13}=\frac{24}{39}+\frac{26}{39} \\ =\frac{24+26}{39} \\ =\frac{50}{39} \end{gathered}$$

(iv)

$$\begin{gathered} \frac{4}{5}+\frac{7}{15} \\ \mathrm{LCM}\mathrm{of}5\&15\mathrm{is}15,\mathrm{so}\mathrm{we}\mathrm{will}\mathrm{convert}\mathrm{each}\mathrm{fraction}\mathrm{into}\mathrm{an}\mathrm{equaivalent}\mathrm{fraction}\mathrm{with}\mathrm{denominator}15. \\ \frac{4\times 3}{5\times 3}+\frac{7\times 1}{15\times 1}=\frac{12}{15}+\frac{7}{15} \\ =\frac{12+7}{15}=\frac{19}{15} \end{gathered}$$