Question

Simplify:

(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
(ii) $\frac{5}{8}+\frac{2}{5}+\frac{3}{4}$
(iii) $\frac{3}{10}+\frac{7}{15}+\frac{3}{5}$
(iv) $\frac{3}{4}+\frac{7}{16}+\frac{5}{8}$
(v) $4\frac{2}{3}+3\frac{1}{4}+7\frac{1}{2}$
(vi) $7\frac{1}{3}+3\frac{2}{3}+5\frac{1}{6}$
(vii) $7+\frac{7}{4}+5\frac{1}{6}$
(viii) $\frac{5}{6}+3+\frac{3}{4}$
(ix) $\frac{7}{18}+\frac{5}{6}+1\frac{1}{12}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{2}{3}+\frac{3}{4}+\frac{1}{2} \\ =\frac{2\times 4}{3\times 4}+\frac{3\times 3}{4\times 3}+\frac{1\times 6}{2\times 6}(\mathrm{Because}\mathrm{LCM}\mathrm{of}3,4\&2\mathrm{is}12) \\ =\frac{8}{12}+\frac{9}{12}+\frac{6}{12} \\ =\frac{8+9+6}{12} \\ =\frac{23}{12} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\frac{5}{8}+\frac{2}{5}+\frac{3}{4} \\ =\frac{5\times 5}{8\times 5}+\frac{2\times 8}{5\times 8}+\frac{3\times 10}{4\times 10}(\mathrm{Because}\mathrm{LCM}\mathrm{of}8,5\&4\mathrm{is}40) \\ =\frac{25}{40}+\frac{16}{40}+\frac{30}{40} \\ =\frac{25+16+30}{40} \\ =\frac{71}{40} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\frac{3}{10}+\frac{7}{15}+\frac{3}{5} \\ =\frac{3\times 3}{10\times 3}+\frac{7\times 2}{15\times 2}+\frac{3\times 6}{5\times 6}(\mathrm{Because}\mathrm{LCM}\mathrm{of}10,15\&5\mathrm{is}30) \\ =\frac{9}{30}+\frac{14}{30}+\frac{18}{30} \\ =\frac{9+14+18}{30} \\ =\frac{41}{30} \end{gathered}$$


$$\begin{gathered} \left(\mathrm{iv}\right)\frac{3}{4}+\frac{7}{16}+\frac{5}{8} \\ =\frac{3\times 4}{4\times 4}+\frac{7\times 1}{16\times 1}+\frac{5\times 2}{8\times 2}(\mathrm{Because}\mathrm{LCM}\mathrm{of}4,16\&8\mathrm{is}16) \\ =\frac{12}{16}+\frac{7}{16}+\frac{10}{16} \\ =\frac{12+7+10}{16} \\ =\frac{29}{16} \end{gathered}$$


$$\begin{gathered} \left(\mathrm{v}\right)4\frac{2}{3}+3\frac{1}{4}+7\frac{1}{2} \\ =\frac{4\times 3+2}{3}+\frac{3\times 4+1}{4}+\frac{7\times 2+1}{2} \\ =\frac{14}{3}+\frac{13}{4}+\frac{15}{2} \\ =\frac{14\times 4}{3\times 4}+\frac{13\times 3}{4\times 3}+\frac{15\times 6}{2\times 6}(\mathrm{Because}\mathrm{LCM}\mathrm{of}3,4\&2\mathrm{is}12) \\ =\frac{56}{12}+\frac{39}{12}+\frac{90}{12} \\ =\frac{56+39+90}{12} \\ =\frac{185}{12} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)7\frac{1}{3}+3\frac{2}{4}+5\frac{1}{6} \\ =\frac{7\times 3+1}{3}+\frac{3\times 4+2}{4}+\frac{5\times 6+1}{6} \\ =\frac{22}{3}+\frac{14}{4}+\frac{31}{6} \\ =\frac{22\times 4}{3\times 4}+\frac{14\times 3}{4\times 3}+\frac{31\times 2}{6\times 2}(\mathrm{Because}\mathrm{LCM}\mathrm{of}3,4\&6\mathrm{is}12) \\ =\frac{88}{12}+\frac{42}{12}+\frac{62}{12} \\ =\frac{88+42+62}{12} \\ =\frac{192÷12}{12÷12}=16(\mathrm{HCF}\mathrm{of}\mathrm{numerator}\&\mathrm{denominator}\mathrm{is}12) \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vii}\right)7+\frac{7}{4}+5\frac{1}{6} \\ \frac{7}{1}+\frac{7}{4}+\frac{5\times 6+1}{6}=\frac{7}{1}+\frac{7}{4}+\frac{31}{6} \\ =\frac{7\times 12}{1\times 12}+\frac{7\times 3}{4\times 3}+\frac{31\times 2}{6\times 2}(\mathrm{Because}\mathrm{LCM}\mathrm{of}1,4\&6\mathrm{is}12) \\ =\frac{84}{12}+\frac{21}{12}+\frac{62}{12} \\ \frac{84+21+62}{12} \\ =\frac{167}{12} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{viii}\right)\frac{5}{6}+3+\frac{3}{4} \\ \frac{5\times 2}{6\times 2}+\frac{3\times 12}{1\times 12}+\frac{3\times 3}{4\times 3}(\mathrm{Because}\mathrm{LCM}\mathrm{of}6,1\&4\mathrm{is}12) \\ =\frac{10}{12}+\frac{36}{12}+\frac{9}{12} \\ =\frac{10+36+9}{12} \\ =\frac{55}{12} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ix}\right)\frac{7}{18}+\frac{5}{6}+1\frac{1}{12} \\ \frac{7}{18}+\frac{5}{6}+\frac{12\times 1+1}{12}=\frac{7}{18}+\frac{5}{6}+\frac{13}{12} \\ =\frac{7\times 2}{18\times 2}+\frac{5\times 6}{6\times 6}+\frac{13\times 3}{12\times 3} \\ =\frac{14}{36}+\frac{30}{36}+\frac{39}{36} \\ =\frac{14+30+39}{36} \\ =\frac{83}{36} \end{gathered}$$