Multiply and reduce to lowest form (if\ possible):
(i) $\frac{2}{3}\times2\frac{2}{3}$
(ii) $\frac{2}{7}\times\frac{7}{9}$
(iii) $\frac{3}{8}\times\frac{6}{4}$
(iv) $\frac{9}{5}\times\frac{3}{5}$
(v) $\frac{1}{3}\times\frac{15}{8}$
(vi) $\frac{11}{2}\times\frac{3}{10}$
(vii) $\frac{4}{5}\times\frac{12}{7}$

To do:

We have to multiply and reduce to lowest form:

(i) $\frac{2}{3}\times2\frac{2}{3}$     

(ii) $\frac{2}{7}\times\frac{7}{9}$

(iii) $\frac{3}{8}\times\frac{6}{4}$   

(iv) $\frac{9}{5}\times\frac{3}{5}$

(v) $\frac{1}{3}\times\frac{15}{8}$     

(vi) $\frac{11}{2}\times\frac{3}{10}$

(vii) $\frac{4}{5}\times\frac{12}{7}$

Solution:

We know that,

$\frac{a}{b}\times\frac{c}{d}=\frac{a \times c}{b \times d}$

Therefore,

(i) $\frac{2}{3}\times2\frac{2}{3}=\frac{2}{3}\times\frac{2\times3+2}{3}$

$=\frac{2}{3}\times\frac{6+2}{3}$

$=\frac{2}{3}\times\frac{8}{3}$

$=\frac{2\times8}{3\times3}$

$=\frac{16}{9}$

(ii) $\frac{2}{7}\times\frac{7}{9}=\frac{2\times7}{7\times9}$

$=\frac{2}{9}$

(iii) $\frac{3}{8}\times\frac{6}{4}=\frac{3\times6}{8\times4}$

$=\frac{3\times3}{4\times4}$

$=\frac{9}{16}$

(iv) $\frac{9}{5}\times\frac{3}{5}=\frac{9\times3}{5\times5}$

$=\frac{27}{25}$

(v) $\frac{1}{3}\times\frac{15}{8}=\frac{1\times15}{3\times8}$

$=\frac{1\times5}{1\times8}$

$=\frac{5}{8}$

(vi) $\frac{11}{2}\times\frac{3}{10}=\frac{11\times3}{2\times10}$

$=\frac{33}{20}$

(vii) $\frac{4}{5}\times\frac{12}{7}=\frac{4\times12}{5\times7}$

$=\frac{48}{35}$

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Updated on: 10-Oct-2022

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