Tag: multiplication of a fraction

Let the money with the man at first be Rs 1
$\displaystyle \therefore $ Money spent=$\displaystyle \frac{5}{6}of Rs1=Rs\frac{5}{6}$
Remaining money=$\displaystyle =1-\frac{5}{6}=Rs\frac{1}{6}$
Money earned$\displaystyle =\frac{1}{2}=Rs\frac{1}{6}=Rs \frac{1}{12}$
$\displaystyle \therefore $ Total money with him now=Rs$\displaystyle \frac{1}{6}+Rs.\frac{1}{12}=Rs.\frac{3}{12}=Rs.\frac{1}{4}$
$\displaystyle \therefore \frac{1}{4}th$ part of the money is with him now

$15$ of $\cfrac{1}{5}=15\times\cfrac{1}{5}=3$

The reciprocal of a number is just divide 1 by the number.
$\therefore$ Reciprocal of $3\cfrac 12$ i.e $\cfrac 72$ is $\cfrac 27$
Option B is correct.

Any number multiplied with $0$ gives $0$. 

The given question shows the associative property of multiplication i.e. 

We need to find product of $\displaystyle \frac {12}{24}, \frac {36}{72}$

$3\dfrac12=\dfrac {3\times 2+1}{2}=\dfrac72$

$0.0777\,=\,7\,\times\,0.111$
$=\,7\,\times\, \displaystyle\frac{1}{9}\,=\, \displaystyle\frac{7}{9}$

The product of rational number with its reciprocal is always equal to $1$.