Question

Find the difference of:

(i) $\frac{13}{24}\mathrm{and}\frac{7}{16}$
(ii) $\frac{5}{18}\mathrm{and}\frac{4}{15}$
(iii) $\frac{1}{12}\mathrm{and}\frac{3}{4}$
(iv) $\frac{2}{3}\mathrm{and}\frac{6}{7}$

Answer 1

(i)
$$\begin{gathered} \frac{13}{24}-\frac{7}{16} \\ =\frac{13\times 2}{24\times 2}-\frac{7\times 3}{16\times 3}(\mathrm{Because}\mathrm{LCM}\mathrm{of}24\&16\mathrm{is}48) \\ =\frac{26}{48}-\frac{21}{48} \\ =\frac{26-21}{48}=\frac{5}{48} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{5}{18}-\frac{4}{15} \\ =\frac{5\times 5}{18\times 5}-\frac{4\times 6}{15\times 6} \\ =\frac{25}{90}-\frac{24}{90}(\mathrm{Because}\mathrm{LCM}\mathrm{of}18\&15\mathrm{is}90) \\ =\frac{25-24}{90}=\frac{1}{90} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{3}{4}-\frac{1}{12} \\ =\frac{3\times 3}{4\times 3}-\frac{1\times 1}{12\times 1}(\mathrm{Because}\mathrm{LCM}\mathrm{of}4\&12\mathrm{is}12) \\ =\frac{9}{12}-\frac{1}{12} \\ =\frac{9-1}{12}=\frac{8}{12} \end{gathered}$$

(iv)
$$\begin{gathered} \frac{6}{7}-\frac{2}{3} \\ =\frac{6\times 3}{7\times 3}-\frac{2\times 7}{3\times 7}(\mathrm{Because}\mathrm{LCM}\mathrm{of}7\&3\mathrm{is}21) \\ =\frac{18}{21}-\frac{14}{21} \\ =\frac{18-14}{21} \\ =\frac{4}{21} \end{gathered}$$