Question

What is $\dfrac{1}{3}$ of 24?

Answer 1

Hint: We are asked to find the value of a fractional part of 24, specifically, $\dfrac{1}{3}$ of 24. To do this, first we will use the fractional rule to get 24 in the numerator and 3 in the denominator. Next, we will split 24 into its factors and then cancel out common terms to obtain the final result.

Complete step by step solution:
In the question, we have been asked to find the value of $\dfrac{1}{3}$ of 24. First, using the property of fractions, we can write $\dfrac{1}{3}$ of 24 as follows, assuming a and b are two positive integers, we can write, $\dfrac{1}{a}$ of b as, $\dfrac{b}{a}$ . Therefore, we can write the value of $\dfrac{1}{3}$ of 24 as, $\dfrac{24}{3}$ .
Next, we will find the factors of 24 and express it in terms of the factors. The factors of 24 are as follows,
$24=3\times 2\times 2\times 2$
Hence, in the next step we can cancel out 3 from both the numerator and the denominator. Doing so, we get the answer,
$\begin{align}
  & \dfrac{24}{3}=\dfrac{3\times 2\times 2\times 2}{3} \\
 & \dfrac{24}{3}=8 \\
\end{align}$
Hence, $\dfrac{1}{3}$ of 24 is found to be equal to 8.

Note: When we find a fractional part of a number, it may not always give us a whole number, but can end up as fractions. For example, if we were asked the value of $\dfrac{1}{15}$ of 24, we find the factors of both numerator and denominator and cancel out the common ones.
$\begin{align}
  & 15=3\times 5 \\
 & 24=3\times 8 \\
\end{align}$
Therefore, we get $\dfrac{1}{15}$ of 24 as,
$\begin{align}
  & \dfrac{24}{15}=\dfrac{3\times 8}{3\times 5} \\
 & \dfrac{24}{15}=\dfrac{8}{5} \\
\end{align}$
$\dfrac{8}{5}$ cannot be further simplified hence we get a fraction as the answer.