Question 188275
In order to multiply fractions, they must either be normal fractions like {{{1/2}}} or {{{2/3}}} or they must be improper fractions. 



So we must convert {{{4&1/5}}} into an improper fraction



Remember, *[Tex \LARGE a \ \frac{b}{c}=\frac{a\cdot c+b}{c}] where "a" is the whole part of the fraction, "b" is the numerator, and "c" is the denominator.


So this means that 


*[Tex \LARGE 4 \frac{1}{5}=\frac{4\cdot5+1}{5}=\frac{20+1}{5}=\frac{21}{5}]



In short *[Tex \LARGE 4 \frac{1}{5}=\frac{21}{5}] which means that the mixed fraction 4 and one fifth is the same as the improper fraction {{{21/5}}}



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*[Tex \LARGE 4 \frac{1}{5} \times \frac{10}{21} \times \frac{9}{20}] ... Start with the given expression.



*[Tex \LARGE \frac{21}{5} \times \frac{10}{21} \times \frac{9}{20}] ... Replace {{{4&1/5}}} with {{{21/5}}}



*[Tex \LARGE \frac{21}{5} \times \frac{10}{21} \times \frac{9}{2\cdot10}] ... Factor 20 into {{{2*10}}}



*[Tex \LARGE \frac{\sout{21}}{5} \times \frac{\sout{10}}{\sout{21}} \times \frac{9}{2\cdot\sout{10}}] ... Cancel out the common terms.




*[Tex \LARGE \frac{1}{5} \times \frac{1}{1} \times \frac{9}{2\cdot1}] ... Simplify



*[Tex \LARGE \frac{1}{5} \times \frac{1}{1} \times \frac{9}{2}] ... Multiply



*[Tex \LARGE \frac{9}{5\cdot2}] ... Combine the fractions.



*[Tex \LARGE \frac{9}{10}] ... Multiply



So *[Tex \LARGE 4 \frac{1}{5} \times \frac{10}{21} \times \frac{9}{20}=\frac{9}{10}]