Question

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

Answer 1

(i)

$$\begin{gathered} \frac{5}{8}+\frac{3}{10} \\ LCMof8,10is40. \\ \Rightarrow \frac{(5\times 5)+(3\times 4)}{40}=\frac{37}{40} \end{gathered}$$
(ii)

$$\begin{gathered} 4\frac{3}{4}+9\frac{2}{5}or\frac{(4\times 4)+3}{4}+\frac{(9\times 5)+2}{5} \\ \Rightarrow \frac{19}{4}+\frac{47}{5} \\ LCMof5,4is20. \\ \frac{(19\times 5)+(47\times 4)}{20}=\frac{283}{20} \end{gathered}$$
(iii)

$$\begin{gathered} \frac{5}{6}+3+\frac{3}{4} \\ LCMof6,4is24. \\ \frac{(5\times 4)+(3\times 24)+(3\times 6)}{24}=\frac{110}{24} \end{gathered}$$
(iv)

$$\begin{gathered} 2\frac{3}{5}+4\frac{7}{10}+2\frac{4}{15}or\frac{(2\times 5)+3}{5}+\frac{(4\times 10)+7}{10}+\frac{(2\times 15)+4}{15} \\ \Rightarrow \frac{13}{5}+\frac{47}{10}+\frac{34}{15} \\ LCMof15,10and5is30. \\ \frac{(13\times 6)+(47\times 3)+(34\times 2)}{30}=\frac{287}{30} \end{gathered}$$