What is 1/6 divided by 1/3?

Hint: To find value when 1/6 is divided by 1/3, we have to represent it in the form \[\dfrac{1}{6}\div \dfrac{1}{3}\] . Then, we have to change the division sign into a multiplication sign. Meanwhile, we have to take the reciprocal of the divisor. Then, we have to simplify.

Complete step-by-step solution:
We have to find the value when 1/6 is divided by 1/3. We can represent this division as
\[\dfrac{1}{6}\div \dfrac{1}{3}\] . Now, to divide , we have to change the division sign ( $\div $ ) into multiplication sign (x). Along with this, we have to take the reciprocal of the divisor. Let us consider a number in fractional form $\dfrac{a}{b}$. Reciprocal is obtained by exchanging the numerator and denominator, that is, $\dfrac{b}{a}$ . Hence, we can write
\[\begin{align}
  & \dfrac{1}{6}\div \dfrac{1}{3} \\
 & =\dfrac{1}{6}\times 3 \\
\end{align}\]
Now, we can cancel the common factor 3.
$\Rightarrow \dfrac{1}{2}$
Hence, 1/6 divided by 1/3 is 1/2.

Note: Students must never forget to take the reciprocal of the divisor after changing the division sign. Reciprocal of a number is actually 1 divided by the number. In the given problem, reciprocal of 1/3 is actually found by dividing 1 by 1/3.
$\Rightarrow \dfrac{1}{\dfrac{1}{3}}=1\times 3=3$
Reciprocal can also be shown as a power of -1. Let us consider 1/3. Reciprocal of 1/3 can also be denoted as
 ${{\left( \dfrac{1}{3} \right)}^{-1}}=\dfrac{1}{\dfrac{1}{3}}=3$
Reciprocal is also known as the multiplicative inverse.
We can also find 1/6 divided by 1/3 by writing it in the form
$\dfrac{\dfrac{1}{6}}{\dfrac{1}{3}}$
We have to take the fractional denominator to the numerator by multiplying the reciprocal of the denominator with the numerator.
$\Rightarrow \dfrac{1}{6}\times 3=\dfrac{1}{2}$