Question

Find the difference of
(i) $\frac{13}{24}\mathrm{and}\frac{7}{16}$
(ii) $6\mathrm{and}\frac{23}{3}$
(iii) $\frac{21}{25}\mathrm{and}\frac{18}{20}$
(iv) $3\frac{3}{10}\mathrm{and}2\frac{7}{15}$

Answer 1

(i)

$$\begin{gathered} \frac{13}{24}-\frac{7}{16} \\ LCMof24and16is48. \\ \frac{(13\times 2)-(7\times 3)}{48}=\frac{5}{48} \end{gathered}$$

(ii)

$$\begin{gathered} \frac{23}{3}-6 \\ LCMof3and1is3. \\ \frac{(23\times 1)-(6\times 3)}{3}=\frac{5}{3} \end{gathered}$$

(iii)

$$\begin{gathered} \frac{18}{20}-\frac{21}{25} \\ LCMof20,25is100. \\ \Rightarrow \frac{(18\times 5)-(21\times 4)}{100}=\frac{6}{100}=\frac{3}{50} \end{gathered}$$

(iv)

$$\begin{gathered} 3\frac{3}{10}-2\frac{7}{15}\iff \frac{(3\times 10)+3}{10}-\frac{(2\times 15)+7}{15}\iff \frac{33}{10}-\frac{37}{15} \\ LCMof10and15is30. \\ \frac{(33\times 3)-(37\times 2)}{30}=\frac{25}{30}\iff \frac{5}{6} \end{gathered}$$