Question

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

Answer 1

(i)

$$\begin{gathered} \frac{2}{3}+\frac{1}{6}-\frac{2}{9} \\ \mathrm{LCM}\mathrm{of}3.6\mathrm{and}9\mathrm{is}18. \\ =\frac{2}{3}+\frac{1}{6}-\frac{2}{9} \\ =\frac{(2\times 6)+(1\times 3)-(2\times 2)}{18} \\ =\frac{11}{18} \end{gathered}$$
(ii)

$$\begin{gathered} 12-3\frac{1}{2}=\frac{12}{1}-\frac{(3\times 2)+1}{2} \\ \mathrm{LCM}\mathrm{of}2\mathrm{and}1\mathrm{is}2. \\ =\frac{12}{1}-\frac{7}{2} \\ =\frac{(12\times 2)-(7\times 1)}{2} \\ =\frac{17}{2} \end{gathered}$$

(iii)

$$\begin{gathered} 7\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}=\frac{(7\times 6)+5}{6}-\frac{(4\times 8)+3}{8}+\frac{(2\times 12)+7}{12} \\ \mathrm{LCM}\mathrm{of}6,8\mathrm{and}12\mathrm{is}24. \\ =\frac{47}{6}-\frac{35}{8}+\frac{31}{12} \\ =\frac{(47\times 4)-(35\times 3)+(31\times 2)}{24} \\ =\frac{145}{24} \end{gathered}$$