Question

How do you find the quotient of $3\dfrac{1}{2}$ divided by 21?

Answer 1

Hint: When we divide a by b let take the value of $\dfrac{a}{b}$ as x which is not an integer so the quotient here will not be equal to x , quotient here will be equal to $\left[ x \right]$ . $\left[ x \right]$ is the greatest integer function of x , it is the greatest integer which is less than or equal to x. we can apply this method to solve the above question.

Complete step by step answer:
We have find the quotient of $3\dfrac{1}{2}$ divided by 21
We can write $3\dfrac{1}{2}$ as $\dfrac{7}{2}$
When we divide a by b the quotient will be $\left[ \dfrac{a}{b} \right]$ where $\left[ {} \right]$ denote greatest integer function
So the quotient when we divide $3\dfrac{1}{2}$ by 21 is $\left[ \dfrac{\left( \dfrac{7}{2} \right)}{21} \right]$
$\Rightarrow \dfrac{\left( \dfrac{7}{2} \right)}{21}=\dfrac{1}{6}$
So the quotient is $\left[ \dfrac{1}{6} \right]$
The value of $\left[ \dfrac{1}{6} \right]$ is the greatest integer which is less than or equal to $\dfrac{1}{6}$ . so we can evaluate $\left[ \dfrac{1}{6} \right]=0$ because 0 is greatest integer which is less than or equal to $\dfrac{1}{6}$ .
So the value of the quotient is 0 when we divide $3\dfrac{1}{2}$ by 21.
Remainder is $\dfrac{1}{6}$ in this case

Note:
Always remember that in a division dividend= (divisor $\times $ quotient) +remainder where quotient is $\left[ \dfrac{Dividend}{divisor} \right]$ . The greatest integer function of a number is the greatest integer that less than or equal to the number for example $\left[ 2.3 \right]=2$ , $\left[ -1.5 \right]=-2$ , $\left[ -3.2 \right]=-4$ . The value of remainder = dividend- (divisor $\times $ quotient).In the above question we have answer what is the result of the division the answer would have $\dfrac{1}{6}$ .