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Multiply the following fractions:
(i) $\frac{2}{5}\times5\frac{1}{4}$
(ii) $6\frac{2}{5}\times\frac{7}{9}$
(iii) $\frac{3}{2}\times5\frac{1}{3}$
(iv) $\frac{5}{6}\times2\frac{3}{7}$
(v) $3\frac{2}{5}\times\frac{4}{7}$
(vi) $2\frac{3}{5}\times3$
(vii) $3\frac{4}{7}\times\frac{3}{5}$
To do:
We have to multiply the given fractions.
(i) $\frac{2}{5}\times5\frac{1}{4}$
(ii) $6\frac{2}{5}\times\frac{7}{9}$
(iii) $\frac{3}{2}\times5\frac{1}{3}$
(iv) $\frac{5}{6}\times2\frac{3}{7}$
(v) $3\frac{2}{5}\times\frac{4}{7}$
(vi) $2\frac{3}{5}\times3$
(vii) $3\frac{4}{7}\times\frac{3}{5}$
Solution:
We know that,
$\frac{a}{b}\times\frac{c}{d}=\frac{a \times c}{b \times d}$
Therefore,
(i) $\frac{2}{5}\times5\frac{1}{4}=\frac{2}{5}\times\frac{(5\times4+1)}{4}$
$=\frac{2}{5}\times\frac{20+1}{4}$
$=\frac{2}{5}\times\frac{21}{4}$
$=\frac{2\times21}{5\times4}$
$=\frac{1\times21}{5\times2}$
$=\frac{21}{10}$
(ii) $6\frac{2}{5}\times\frac{7}{9}=\frac{6\times5+2}{5}\times\frac{7}{9}$
$=\frac{30+2}{5}\times\frac{7}{9}$
$=\frac{32}{5}\times\frac{7}{9}$
$=\frac{32\times7}{5\times9}$
$=\frac{224}{45}$
(iii) $\frac{3}{2}\times5\frac{1}{3}=\frac{3}{2}\times\frac{(5\times3+1)}{3}$
$=\frac{3}{2}\times\frac{15+1}{3}$
$=\frac{3}{2}\times\frac{16}{3}$
$=\frac{3\times16}{2\times3}$
$=\frac{1\times8}{1\times1}$
$=8$
(iv) $\frac{5}{6}\times2\frac{3}{7}=\frac{5}{6}\times\frac{(2\times7+3)}{7}$
$=\frac{5}{6}\times\frac{14+3}{7}$
$=\frac{5}{6}\times\frac{17}{7}$
$=\frac{5\times17}{6\times7}$
$=\frac{85}{42}$
(v) $3\frac{2}{5}\times\frac{4}{7}=\frac{3\times5+2}{5}\times\frac{4}{7}$
$=\frac{15+2}{5}\times\frac{4}{7}$
$=\frac{17}{5}\times\frac{4}{7}$
$=\frac{17\times4}{5\times7}$
$=\frac{68}{35}$
(vi) $2\frac{3}{5}\times3=\frac{(2\times5+3)}{5}\times3$
$=\frac{(10+3)}{5}\times3$
$=\frac{13}{5}\times3$
$=\frac{13\times3}{5}$
$=\frac{39}{5}$
(vii) $3\frac{4}{7}\times\frac{3}{5}=\frac{(3\times7+4)}{7}\times\frac{3}{5}$
$=\frac{(21+4)}{7}\times\frac{3}{5}$
$=\frac{25}{7}\times\frac{3}{5}$
$=\frac{25\times3}{7\times5}$
$=\frac{5\times3}{7\times1}$
$=\frac{15}{7}$
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