# Multiply and express as a mixed fraction:(a) $3\times5\frac{1}{5}$(b) $5\times6\frac{3}{4}$(c) $7\times2\frac{1}{4}$(d) $4\times6\frac{1}{3}$(e) $3\frac{1}{4}\times6$(f) $3\frac{2}{5}\times8$

To do:

We have to multiply and express as a mixed fraction.

Solution:

(a) $3\times5\frac{1}{5}= 3\times\frac{5\times5+1}{5}$

$=3\times\frac{25+1}{5}$

$=3\times\frac{26}{5}$

$= \frac{(3\times26)}{5}$

$=\frac{78}{5}$

$\frac{78}{5}$ is an improper fraction

On converting $\frac{78}{5}$ into a mixed fraction, we get

$\frac{78}{5}=\frac{5\times15+3}{5}$

$=15\frac{3}{5}$

(b) $5\times6\frac{3}{4}=5\times\frac{6\times4+3}{4}$

$=5\times\frac{24+3}{4}$

$=5\times\frac{27}{4}$

$= \frac{(5\times27)}{4}$

$= \frac{135}{4}$

$\frac{135}{4}$ is an improper fraction.

On converting $\frac{135}{4}$ into a mixed fraction, we get

$\frac{135}{4}=\frac{4\times33+3}{4}$

$=33\frac{3}{4}$

(c) $7\times2\frac{1}{4}=7\times\frac{2\times4+1}{4}$

$=7\times\frac{8+1}{4}$

$=7\times\frac{9}{4}$

$=\frac{(7\times9)}{4}$

$= \frac{63}{4}$

$\frac{63}{4}$ is an improper fraction.

Converting $\frac{63}{4}$ into a mixed fraction, we get,

$\frac{63}{4}=\frac{4\times15+3}{4}$

$=15\frac{3}{4}$

(d) $4\times6\frac{1}{3}=4\times\frac{6\times3+1}{3}$

$=4\times\frac{18+1}{3}$

$=4\times\frac{19}{3}$

$=\frac{(4\times19)}{3}$

$=\frac{76}{3}$

$\frac{76}{3}$ is an improper fraction.

Converting $\frac{76}{3}$ into a mixed fraction, we get

$\frac{76}{3}=\frac{3\times25+1}{3}$

$=25\frac{1}{3}$

(e) $3\frac{1}{4}\times6=\frac{3\times4+1}{4}\times6$

$=\frac{12+1}{4}\times6$

$=(\frac{13}{4})\times6$

$= \frac{(13\times6)}{4}$

$= \frac{78}{4}$

$=\frac{39}{2}$

$\frac{39}{2}$ is an improper fraction.

Converting $\frac{39}{2}$ into a mixed fraction, we get,

$\frac{39}{2} =\frac{2\times19+1}{2}$

$=19\frac{1}{2}$

(f) $3\frac{2}{5}\times8=\frac{3\times5+2}{5}\times8$

$=\frac{15+2}{5}\times8$

$= (\frac{17}{5})\times8$

$= \frac{(17\times8)}{5}$

$= \frac{136}{5}$

$\frac{136}{5}$ is an improper fraction.

Converting $\frac{136}{5}$ into a mixed fraction, we get

$\frac{136}{5}=\frac{5\times27+1}{5}$

$=27\frac{1}{5}$

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Updated on: 10-Oct-2022

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