Question

What is the value of $\dfrac{1}{3}\div 4$?

Answer 1

Hint: First we will assume the value of the given expression as y. Now, we will consider $\dfrac{1}{3}$ as the dividend and 4 as the divisor. We will take the reciprocal of 4 by interchanging its numerator and denominator and multiply it with $\dfrac{1}{3}$ to get the answer. We will consider the denominator of 4 equal to 1.

Complete step by step answer:
Here we have been asked to find the value of the expression $\dfrac{1}{3}\div 4$. Let us assume the value of this expression as y, so we have,
\[\Rightarrow y=\dfrac{1}{3}\div 4\]
Here we have $\dfrac{1}{3}$ as the dividend while 4 is the divisor. So, to divide a given number/fraction by another number/fraction means, we have to multiply the first number (dividend) with the reciprocal of the second number (divisor). So we need to find the reciprocal of 4 in the 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 4 as $\dfrac{4}{1}$ in the fractional form so inter-changing the numerator (4) and the denominator (1) we get $\dfrac{1}{4}$ as the required reciprocal of divisor. Therefore, multiplying $\dfrac{1}{3}$ with $\dfrac{1}{4}$ and simplifying we get,
\[\begin{align}
  & \Rightarrow y=\dfrac{1}{3}\times \dfrac{1}{4} \\
 & \therefore y=\dfrac{1}{12} \\
\end{align}\]

Hence, $\dfrac{1}{12}$ 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. You must know that division is the inverse process of multiplication and that is why the above approach is used for dividing a fraction with another fraction.