# Find: (a) $\frac{1}{2}$ of (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$(b) $\frac{5}{8}$ of (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$

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To do:

We have to find:

(a) (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$

(b) (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$

Solution:

(a)

(i) $\frac{1}{2}$ of $2\frac{3}{4}$

$2\frac{3}{4}=\frac{2\times4+3}{4}$

$=\frac{8+3}{4}$

$=\frac{11}{4}$

$\frac{1}{2}$ of $2\frac{3}{4}=\frac{1}{2}$ of $\frac{11}{4}$

$=\frac{1}{2}\times\frac{11}{4}$

$=\frac{1\times11}{2\times4}$

$=\frac{11}{8}$

(ii) $\frac{1}{2}$ of $4 \frac{2}{9}$

$4\frac{2}{9}=\frac{4\times9+2}{9}$

$=\frac{36+2}{9}$

$=\frac{38}{9}$

$\frac{1}{2}$ of $4 \frac{2}{9}=\frac{1}{2}$ of $\frac{38}{9}$

$=\frac{1\times38}{2\times9}$

$=\frac{38}{18}$

$=\frac{19}{9}$

(b)

(i) $\frac{5}{8}$ of $3\frac{5}{6}$

$3\frac{5}{6}=\frac{3\times6+5}{6}$

$=\frac{18+5}{6}$

$=\frac{23}{6}$

$\frac{5}{8}$ of $3\frac{5}{6}=\frac{5}{8}\times(\frac{23}{6})$

$=\frac{5\times23}{8\times6}$

$=\frac{115}{48}$

(ii) $\frac{5}{8}$ of $9\frac{2}{3}$

$9\frac{2}{3}=\frac{9\times3+2}{3}$

$=\frac{27+2}{3}$

$=\frac{29}{3}$

$\frac{5}{8}$ of $9\frac{2}{3}=\frac{5}{8}\times\frac{29}{3}$

$=\frac{5\times29}{8\times3}$

$=\frac{145}{24}$

Updated on 10-Oct-2022 13:32:36