Question

Simplify:
(i) $\frac{2}{3}+\frac{5}{6}-\frac{1}{9}$
(ii) $8-4\frac{1}{2}-2\frac{1}{4}$
(iii)$8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}$

Answer 1

(i) Given $\frac{2}{3}+\frac{5}{6}-\frac{1}{9}$
$=\frac{12+15-2}{18}$ [Since LCM of $3,6$ and $9=18$]
$=\frac{27-2}{18}$
$=\frac{25}{18}$
$\therefore \frac{2}{3}+\frac{5}{6}-\frac{1}{9}=1\frac{7}{18}$
(ii)Given $8-4\frac{1}{2}-2\frac{1}{4}$
$=\frac{8}{1}-\frac{9}{2}-\frac{9}{4}$
$=\frac{32-18-9}{4}$ [∵ LCM of $1,2$ and $4=4$]
$=\frac{32-27}{4}$
$=\frac{5}{4}$
$\therefore 8-4\frac{1}{2}-2\frac{1}{4}=1\frac{1}{4}$
(iii) $8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}$
$=\frac{53}{6}-\frac{27}{8}+\frac{19}{12}$
$=\frac{212-81+38}{24}$ [∵ LCM of $6,8$ and $12=24$]
$=\frac{250-81}{24}$
$=\frac{169}{24}$
$\therefore 8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}=7\frac{1}{24}$