Question

How do you simplify the fraction \[\dfrac{2}{24}?\]

Answer 1

Hint: We are given the expression as \[\dfrac{2}{24},\] we are asked to simplify this fraction. To do so we will learn what type of fraction we have depending on the type, we will find the way to solve it. In our fraction, we can see we have a fraction of constant term, we will factor the term in numerator and denominator and then cancel the like terms and the term which is left is our required solution.

Complete step by step answer:
We are given a fraction as \[\dfrac{2}{24},\] we have to simplify. We will understand that different types of fractions have different ways to simplify them. For example, if we have the fraction in solving rational, then to simplify it means we have to remove the radical from the denominator. If the fraction are in the decimal form, so to simplify it means we have to remove their decimal. If the fraction are in exponent form, then to simplify it means we have to reduce them using \[\dfrac{{{x}^{a}}}{{{x}^{b}}}={{x}^{a-b}}\] formula. In our problem, first, have the numerical terms on the numerator and denominator then simplify them means we have to just remove the highest common factor they both have. Now in our fraction, we have 2 in the numerator and 24 in the denominator. They are just numbers, so we have to cancel like the term to simplify our problem. Now, 2 can be factored as \[2\times 1\] while 24 can be factored as \[2\times 2\times 2\times 3.\] So, we can see that they have 2 as common. So, we can cancel it and the remaining will be put in the equation. So,
\[\dfrac{2}{24}=\dfrac{2\times 1}{2\times 2\times 2\times 3}\]
\[\Rightarrow \dfrac{2}{24}=\dfrac{1}{2\times 2\times 3}\]
On solving, we get,
\[\Rightarrow \dfrac{2}{24}=\dfrac{1}{12}\]
So, the simplified form of \[\dfrac{2}{24}\] is \[\dfrac{1}{12}.\]

Note:
Always need to see that we factor always into its prime factor, if we do not factor its prime factor, so maybe we evaluate an incorrect solution. For example, we have \[\dfrac{18}{54}\] so we can write it as \[\dfrac{18}{54}=\dfrac{2\times 9}{2\times 3\times 3\times 3}\] and we can see the same term is only 2. So, we can cancel just 2 only and solve as \[\dfrac{9}{27}\] which is incorrect.