Question

What is half of a half? What is half of that?

Answer 1

Hint: First of all consider the fraction $\dfrac{1}{2}$ as the initial number. Now, multiply it with $\dfrac{1}{2}$ to get its half and the answer to the first part of the question. To multiply two fractions take the product of their numerators to get the resultant numerator and the product of their denominators to get the resultant denominator. Now, again take the product of the obtained fraction with $\dfrac{1}{2}$ to get the answer to the second part of the question.

Complete step by step solution:
Here we have been asked to find the value of half of a half in the first part of the question and again we have to find the half of the resultant number as the second part of the question.
Now, considering the first part of the question we have to find half of a half. Since, we haven't stated if we have to take half of any particular number in the starting so we will consider half of 1, i.e. $\dfrac{1}{2}$. So we have to take half of this fraction, which means the product of $\dfrac{1}{2}$ with $\dfrac{1}{2}$. When we take the product of two fractions we multiply their numerators to get the resultant numerator and the product of their denominators to get the resultant denominator. So we get,
$\begin{align}
 & \Rightarrow \dfrac{1}{2}\times \dfrac{1}{2}=\dfrac{1\times 1}{2\times 2} \\
 & \therefore \dfrac{1}{2}\times \dfrac{1}{2}=\dfrac{1}{4} \\
\end{align}$
Therefore, the answer to the first part of the question is $\dfrac{1}{4}$.
Now, in the second part we have to consider half of $\dfrac{1}{4}$ that means we have to consider the product of $\dfrac{1}{2}$ with $\dfrac{1}{4}$. So we get,
$\begin{align}
 & \Rightarrow \dfrac{1}{4}\times \dfrac{1}{2}=\dfrac{1\times 1}{4\times 2} \\
 & \therefore \dfrac{1}{4}\times \dfrac{1}{2}=\dfrac{1}{8} \\
\end{align}$

Therefore, the answer to the second part of the question is $\dfrac{1}{8}$.

Note: Remember the rules of multiplying two fractions. Never consider the product of a numerator of one fraction with the denominator of the other fraction. Also, take a note that here we do not have any common factors to cancel in the numerator and denominator but whenever there is you must cancel them and write the final answer in the simplest form.