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Multiply and express as a mixed fraction: (a) 3 multiplied by 5 1/5

6. Multiply and express as a mixed fraction :

      (a) 3\times 5\frac{1}{5}                  (b) 5\times 6\frac{3}{4}                      (c) 7\times 2\frac{1}{4}

      (d) 4\times 6\frac{1}{3}                  (e) 3\frac{1}{4}\times 6                      (f) 3\frac{2}{5}\times 8     

 

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(a) 3\times 5\frac{1}{5}

On Multiplying, we get

\Rightarrow 3\times\frac{5\times5+1}{5}=3\times\frac{26}{5}=\frac{3\times26}{5}=\frac{78}{5}

Converting This into Mixed Fraction,

\Rightarrow \frac{78}{5}=\frac{75+3}{5}=\frac{75}{5}+\frac{3}{5}=15+\frac{3}{5}=15\frac{3}{5}

(b) 5\times 6\frac{3}{4}

On Multiplying, we get

\Rightarrow 5\times\frac{6\times4+3}{4}=5\times\frac{27}{4}=\frac{5\times27}{4}=\frac{135}{4}

Converting This into Mixed Fraction,

\Rightarrow \frac{135}{4}=\frac{132+3}{4}=\frac{132}{4}+\frac{3}{4}=33+\frac{3}{4}=33\frac{3}{4}

(c) 7\times 2\frac{1}{4}

On multiplying, we get 

7\times 2\frac{1}{4}=7\times \frac{4\times2+1}{4}=7\times\frac{9}{4}=\frac{7\times9}{4}=\frac{63}{4}

Converting it into a mixed fraction, we get 

\frac{63}{4}=\frac{60+3}{4}=\frac{60}{4}+\frac{3}{4}=15+\frac{3}{4}=15\frac{3}{4}

(d) 4\times 6\frac{1}{3}

On multiplying, we get 

4\times 6\frac{1}{3}=4\times\frac{3\times6+1}{3}=4\times\frac{19}{3}=\frac{4\times 19}{3}=\frac{76}{3}

Converting it into a mixed fraction,

\frac{76}{3}=\frac{75+1}{3}=\frac{75}{3}+\frac{1}{3}=25+\frac{1}{3}=25\frac{1}{3}

(e) 3\frac{1}{4}\times 6

Multiplying them, we get

3\frac{1}{4}\times 6=\frac{4\times3+1}{4}\times6=\frac{13}{4}\times6=\frac{13\times6}{4}=\frac{78}{4}

Now, converting the result fraction we got to mixed fraction,

\frac{78}{4}=\frac{76+2}{4}=\frac{76}{4}+\frac{2}{4}=19+\frac{1}{2}=19\frac{1}{2}

(f) 3\frac{2}{5}\times 8

On multiplying, we get

3\frac{2}{5}\times 8=\frac{5\times3+2}{5}\times8=\frac{17}{5}\times8=\frac{17\times8}{5}=\frac{136}{5}

Converting this into a mixed fraction, we get 

\frac{136}{5}=\frac{135+1}{5}=\frac{135}{5}+\frac{1}{5}=27+\frac{1}{5}=27\frac{1}{5}

 

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