Question

What is 11 divided by 12 as a fraction?

Answer 1

Hint: Whenever a is divided by b, we can express this a fraction $\dfrac{a}{b}$ . We should further simplify the fraction into its simplest form. To change into the simplest form, we should find the HCF of a and b, and then separately divide both the numerator and denominator with this HCF. The evaluated fraction will then be in its simplest form.

Complete step by step solution:
We know by the definition of fraction that $\dfrac{a}{b}$ is nothing but a divided by b.
Thus, by the converse of this definition, we can say that a divided by b is the same as $\dfrac{a}{b}$ .
Hence, we can also say that 11 divided by 12 is the same as $\dfrac{11}{12}$ .
Now, this fraction is already in its simplest form, since it has no common factor other than 1.
This could also be verified by finding the HCF (Highest Common Factor) or GCD (Greatest Common Divisor).
Prime factorisation of 11 and 12 are shown below,
$\begin{align}
  & 11\left| \!{\underline {\,
  11 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1\text{ } \,}} \right. \\
\end{align}$
And
$\begin{align}
  & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6\text{ } \,}} \right. \\
 & 3\left| \!{\underline {\,
  3\text{ } \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Thus,
$\begin{align}
  & 11=11\times 1 \\
 & 12=3\times 2\times 2\times 1 \\
\end{align}$
We can see that 11 and 12 have no other common factor other than 1.
Thus, HCF of 11 and 12 is 1. This further confirms the fact that the fraction is already in its simplest form.
If the fraction hadn’t been in its simplest form, we would have divided the numerator and denominator by HCF, and we would have got the simplest form of our fraction.
Hence, 11 divided by 12 is $\dfrac{11}{12}$ as a fraction.

Note: We should take care that the dividend becomes numerator, and the divisor becomes denominator, and not vice versa. We must not forget to convert the fraction into its simplest form. Some students can make silly mistakes while reading the question and give wrong answers in decimal form instead of fraction form. So, they must read the question carefully before attempting it.