Question

Simplify:
(i) $\frac{11}{12}÷(\frac{5}{9}\times \frac{18}{25})$

(ii) $(2\frac{1}{2}\times \frac{8}{10})÷(1\frac{1}{2}+\frac{5}{8})$

(iii) $\frac{15}{16}$ of $(\frac{5}{6}-\frac{1}{2})÷\frac{10}{11}$

(iv) $\frac{9}{8}÷\frac{3}{5}$ of $(\frac{3}{4}+\frac{3}{5})$

(v) $\frac{2}{5}÷\{\frac{1}{5}of[\frac{3}{4}-\frac{1}{2}]-1\}$

(vi) $(1\frac{3}{4}\times 3\frac{1}{7})-(4\frac{3}{8}÷5\frac{3}{5})$

Answer 1

(i) $\frac{11}{12}÷(\frac{5}{9}\times \frac{18}{25})$

$\Rightarrow \frac{11}{12}÷\left(\frac{2}{5}\right)$

$\Rightarrow \frac{11}{12}\times \left(\frac{5}{2}\right)$

$\Rightarrow \frac{55}{24}$

(ii) $(2\frac{1}{2}\times \frac{8}{10})÷(1\frac{1}{2}+\frac{5}{8})$

$\Rightarrow (\frac{5}{2}\times \frac{8}{10})÷(\frac{3}{2}+\frac{5}{8})$

$\Rightarrow \left(2\right)÷\left(\frac{12+5}{8}\right)$

$\Rightarrow \left(2\right)÷\left(\frac{13}{8}\right)$

$\Rightarrow 2\times \left(\frac{8}{13}\right)$

$\Rightarrow \frac{16}{13}$

(iii) $\frac{15}{16}$ of $(\frac{5}{6}-\frac{1}{2})÷\frac{10}{11}$

$\Rightarrow \frac{15}{16}$ of $\left(\frac{5-3}{6}\right)÷\frac{10}{11}$

$\Rightarrow \frac{15}{16}\times \left(\frac{3}{6}\right)÷\frac{10}{11}$

$\Rightarrow \frac{15}{16}\times \left(\frac{1}{2}\right)\times \frac{11}{10}$

$\Rightarrow \frac{3}{16}\times \left(\frac{1}{2}\right)\times \frac{11}{2}$

$\Rightarrow \frac{33}{64}$

(iv) $\frac{9}{8}÷\frac{3}{5}$ of $(\frac{3}{4}+\frac{3}{5})$

$\Rightarrow \frac{9}{8}\times \frac{5}{3}\times \left(\frac{15+12}{20}\right)$

$\Rightarrow \frac{15}{8}\times \left(\frac{27}{20}\right)$

$\Rightarrow \frac{3}{8}\times \left(\frac{27}{4}\right)$

$\Rightarrow \frac{81}{32}$

(v) $\frac{2}{5}÷\{\frac{1}{5}of[\frac{3}{4}-\frac{1}{2}]-1\}$

$\Rightarrow \frac{2}{5}÷\{\frac{1}{5}\times \left[\frac{3-2}{4}\right]-1\}$

$\Rightarrow \frac{2}{5}÷\{\frac{1}{5}\times \left[\frac{1}{4}\right]-1\}$

$\Rightarrow \frac{2}{5}÷\{\frac{1}{20}-1\}$

$\Rightarrow \frac{2}{5}÷\left\{\frac{-19}{20}\right\}$

$\Rightarrow \frac{2}{5}\times \{-\frac{20}{19}\}$

$\Rightarrow -\frac{8}{19}$

(vi) $(1\frac{3}{4}\times 3\frac{1}{7})-(4\frac{3}{8}÷5\frac{3}{5})$

$\Rightarrow (\frac{7}{4}\times \frac{22}{7})-(\frac{35}{8}÷\frac{28}{5})$

$\Rightarrow \left(\frac{11}{2}\right)-(\frac{35}{8}\times \frac{5}{28})$

$\Rightarrow \left(\frac{11}{2}\right)-(\frac{5}{8}\times \frac{5}{4})$

$\Rightarrow \left(\frac{11}{2}\right)-\left(\frac{25}{32}\right)$

$\Rightarrow \left(\frac{176-25}{32}\right)$

$\Rightarrow \frac{151}{32}$

Hence, this is the answer.