Question

Find the sum:

(i)
(ii)
(iii)
(iv)
(v)
(vi)

Answer 1

(i) $\frac{5}{9}+\frac{3}{9}=\frac{8}{9}$

(ii) $\frac{8}{9}+\frac{7}{12}$

$=\frac{32}{36}+\frac{21}{36}$ [∵ LCM of 9 and 12 = 36]

= $\frac{32+21}{36}$

= $\frac{53}{36}=1\frac{17}{36}$

(iii) $\frac{5}{6}+\frac{7}{8}$

$=\frac{20}{24}+\frac{21}{24}$ [∵ LCM of 6 and 8 = 24]

= $\frac{20+21}{24}$

=$\frac{41}{24}=1\frac{17}{24}$

(iv) $\frac{7}{12}+\frac{11}{16}+\frac{9}{24}$

$\frac{28}{48}+\frac{33}{48}+\frac{18}{48}$ [∵ LCM of 12, 16 and 24 = 48]

= $\frac{28+33+18}{48}$

= $\frac{79}{48}=1\frac{31}{48}$

(v) $3\frac{4}{5}+2\frac{3}{10}+1\frac{1}{15}$

= $\frac{19}{5}+\frac{23}{10}+\frac{16}{15}$

$=\frac{114}{30}+\frac{69}{30}+\frac{32}{30}$ [∵ LCM of 5, 10 and 15 = 30]

= $\frac{114+69+32}{30}$

= $\frac{215}{30}=7\frac{5}{30}=7\frac{1}{6}$

(vi) $8\frac{3}{4}+10\frac{2}{5}$

= $\frac{35}{4}+\frac{52}{5}$

$=\frac{175}{20}+\frac{208}{20}$ [∵ LCM of 4 and 5 = 20]

= $\frac{175+208}{20}$

= $\frac{383}{20}=19\frac{3}{20}$