Question

Find the difference:
(i) $\frac{6}{7}-\frac{9}{11}$
(ii) $8-\frac{5}{9}$
(iii) $9-5\frac{2}{3}$
(iv) $4\frac{3}{10}-1\frac{2}{15}$

Answer 1

(i)
$$\begin{gathered} \frac{6}{7}-\frac{9}{11} \\ LCMof7and11is77. \\ \Rightarrow \frac{6}{7}-\frac{9}{11}\iff \frac{(6\times 11)-(9\times 7)}{77}\iff \frac{3}{77} \end{gathered}$$

(ii)
$$\begin{gathered} 8-\frac{5}{9} \\ LCMof1and9is9. \\ \Rightarrow \frac{8}{1}-\frac{5}{9}\iff \frac{(8\times 9)-(5\times 1)}{9}\iff \frac{67}{9} \end{gathered}$$

(iii)
$$\begin{gathered} 9-5\frac{2}{3}\iff \frac{9}{1}-\frac{(5\times 3)+2}{3} \\ LCMof1and3is3. \\ \Rightarrow \frac{9}{1}-\frac{17}{3}\iff \frac{(9\times 3)-(17\times 1)}{3}\iff \frac{10}{3} \end{gathered}$$

(iv)
$$\begin{gathered} 4\frac{3}{10}-1\frac{2}{15}\iff \frac{(4\times 10)+3}{10}-\frac{(15\times 1)+2}{15} \\ LCMof10and15is30. \\ \Rightarrow \frac{43}{10}-\frac{17}{15}\iff \frac{(43\times 3)-(17\times 2)}{30}\iff \frac{95}{30}\iff \frac{19}{6} \end{gathered}$$