Question

Multiply and reduce to lowest form and convert into a mixed fraction:

(i) $7\times \frac{3}{5}$ (ii) $4\times \frac{1}{3}$
(iii) $2\times \frac{6}{7}$ (iv) $5\times \frac{2}{9}$

(v) $\frac{2}{3}\times 4$ (vi) $\frac{5}{2}\times 6$
(vii) $11\times \frac{4}{7}$ (viii) $20\times \frac{4}{5}$
(ix) $13\times \frac{1}{3}$ (x) $15\times \frac{3}{5}$

Answer 1

The rule of multiplication of a fraction $\left(\frac{p}{q}\right)$ and an integer($z$) is $\frac{p\times \left(z\right)}{q}$.......(i)
i.e., multiplication of numerator and an integer, divided by same denominator
(i) Given $7\times \frac{3}{5}$
$\Rightarrow 7\times \frac{3}{5}=\frac{7\times 3}{5}$
$=\frac{21}{5}$
$=4\frac{1}{5}$

$\therefore 7\times \frac{3}{5}=4\frac{1}{5}$

(ii) Given $4\times \frac{1}{3}$
$\Rightarrow 4\times \frac{1}{3}=\frac{4\times 1}{3}$
$=\frac{4}{3}$
$=1\frac{1}{3}$
$\therefore 4\times \frac{1}{3}=1\frac{1}{3}$

(iii) Given $2\times \frac{6}{7}$
$\Rightarrow 2\times \frac{6}{7}=\frac{2\times 6}{7}$
$=\frac{12}{7}$
$=1\frac{5}{7}$
$\therefore 2\times \frac{6}{7}=1\frac{5}{7}$

(iv) Given $5\times \frac{2}{9}$

$\Rightarrow 5\times \frac{2}{9}=\frac{5\times 2}{9}$
$=\frac{10}{9}$
$=1\frac{1}{9}$
$\therefore 5\times \frac{2}{9}=1\frac{1}{9}$
(v) Given $4\times \frac{2}{3}$
$\Rightarrow 4\times \frac{2}{3}=\frac{4\times 2}{3}$
$=\frac{8}{3}$
$=2\frac{2}{3}$
$\therefore 4\times \frac{2}{9}=2\frac{2}{3}$

(vi) Given $\frac{5}{2}\times 6$
Here $6=2\times 3$
$\frac{5}{2}\times 6=\frac{5}{2}\times (2\times 3)$
$=5\times 3$ [2 got cancelled]
$\therefore \frac{5}{2}\times 6=15$

(vii) Given $11\times \frac{4}{7}$
$\Rightarrow 11\times \frac{4}{7}=\frac{11\times 4}{7}$
$=\frac{44}{7}$
$=6\frac{2}{7}$
$\therefore 11\times \frac{4}{7}=6\frac{2}{7}$

(viii) Given $20\times \frac{4}{5}$
Here, $20=4\times 5$
$\Rightarrow \frac{4}{5}\times 20=\frac{4}{5}\times (4\times 5)$
$=4\times 4$ [$5$ got cancelled]
$\therefore \frac{4}{5}\times 20=16$

(ix) Given $13\times \frac{1}{3}$

$\Rightarrow 13\times \frac{1}{3}=\frac{13\times 1}{3}$
$=\frac{13}{3}$
$=4\frac{1}{3}$
$\therefore 13\times \frac{1}{3}=4\frac{1}{3}$

(x) Given $15\times \frac{3}{5}$
Here, $15=5\times 3$
$\frac{3}{5}\times 15=\frac{3}{5}\times (5\times 3)$
$=3\times 3$ [$5$ got cancelled]
$\therefore 15\times \frac{3}{5}=9$