Question

Simplify:
(i) $\frac{4}{7}÷\frac{9}{14}$
(ii) $\frac{7}{10}÷\frac{3}{5}$
(iii) $\frac{8}{9}÷16$
(iv) $9÷\frac{1}{3}=9\times 3$
(v) $24÷67=24\times \frac{7}{6}$
(vi) $3\frac{3}{5}÷\frac{4}{5}$
(vii) $3\frac{3}{7}÷\frac{8}{21}$
(viii) $5\frac{4}{7}÷\frac{13}{10}$
(ix) $15\frac{3}{7}÷1\frac{23}{49}$

Answer 1

(i) $\frac{4}{7}÷\frac{9}{14}=\frac{4}{7}\times \frac{14}{9}$ [Since, Reciprocal of $\frac{9}{14}=\frac{14}{9}$]
$=\frac{8}{9}$
(ii) $\frac{7}{10}÷\frac{3}{5}=\frac{7}{10}\times \frac{5}{3}$ [Since, Reciprocal of $\frac{3}{5}=\frac{5}{3}$]
$=\frac{7}{6}$
(iii) $\frac{8}{9}÷16=\frac{8}{9}\times \frac{1}{16}$ [Since, Reciprocal of $16=\frac{1}{16}$]
$=\frac{1}{18}$
(iv) $9÷\frac{1}{3}=9\times 3$ [Since, Reciprocal of $\frac{1}{3}=3$]
$=27$
(v) $24÷67=24\times \frac{7}{6}$ [Since, Reciprocal of $\frac{6}{7}=\frac{7}{6}$]
$=4\times 7=28$
(vi) $3\frac{3}{5}÷\frac{4}{5}=\frac{18}{5}÷\frac{4}{5}$
$=\frac{18}{5}\times \frac{5}{4}$ [Since, Reciprocal of $\frac{4}{5}=\frac{5}{4}$]
$=\frac{18}{4}$
$=\frac{9}{2}=4\frac{1}{2}$
(vii) $3\frac{3}{7}÷\frac{8}{21}=\frac{24}{7}÷\frac{8}{21}$
$=\frac{24}{7}\times \frac{21}{8}$
[Since, Reciprocal of $\frac{8}{21}=\frac{2}{18}$]
$=3\times 3$
$=9$
(viii) $5\frac{4}{7}÷\frac{13}{10}=\frac{39}{7}÷\frac{13}{10}$
$=\frac{39}{7}\times \frac{10}{13}$ [Since, Reciprocal of $\frac{13}{10}=\frac{10}{13}$]
$=\frac{30}{7}$
$=4\frac{2}{7}$
(ix) $15\frac{3}{7}÷1\frac{23}{49}=\frac{108}{7}÷\frac{72}{49}$
$=\frac{108}{7}\times \frac{49}{72}$
[ Reciprocal of $\frac{72}{49}=\frac{49}{72}$]
$=\frac{9\times 7}{1\times 6}$
$=\frac{3\times 7}{1\times 2}$
$=\frac{21}{2}=10\frac{1}{2}$