Question

What is the $\dfrac{1}{3}$ divided by 6?

Answer 1

Hint: First we will assume the value of the given expression as x. Now, we will consider $\dfrac{1}{3}$ as the dividend and 6 as the divisor. We will take the reciprocal of 6 by interchanging its numerator and denominator and multiply it with $\dfrac{1}{3}$ to get the answer. We will consider the denominator of 6 equal to 1 so that the number does not get changed.

Complete step by step answer:
Here we have been asked to find the value of the expression $\dfrac{1}{3}$ divided by 6. Let us assume the value of this expression as x, so mathematically we have the expression,
\[\Rightarrow y=\dfrac{1}{3}\div 6\]
Here we have $\dfrac{1}{3}$ as the dividend while 4 is the divisor. The rule to divide a given number/fraction by another number/fraction states that we have to multiply the first number (dividend) with the reciprocal of the second number (divisor). So we need to find the reciprocal of 6 as our first step. The term reciprocal means the inverse of the given number/fraction, obtained by interchanging the numerator and the denominator of the number/fraction.
We can write 6 as $\dfrac{6}{1}$ in the fractional form as 1 in the denominator does not change the value of the divisor, so inter-changing the numerator (6) and the denominator (1) we get $\dfrac{1}{6}$ as the required reciprocal of divisor. Therefore, multiplying $\dfrac{1}{3}$ with $\dfrac{1}{6}$ and simplifying we get,
\[\begin{align}
  & \Rightarrow y=\dfrac{1}{3}\times \dfrac{1}{6} \\
 & \therefore y=\dfrac{1}{18} \\
\end{align}\]

Hence, $\dfrac{1}{18}$ is our answer.

Note: Remember that the product of a number and its reciprocal is always 1. When there is no number present in the denominator then you have to assume the denominator as 1 because multiplying or dividing a number does not change its value which is known as the multiplicative identity because it retains the identity of the original number.