Question

How do you simplify the fraction $\dfrac{{18}}{{24}}$ ?

Answer 1

Hint:
Whenever they give any fraction number and ask us to find the simplest form of that, then we need to find common factor which divides both number that is both numerator and denominator with zero remainder, repeat the same until no common factor except $1$ is achieved, which will be the required simplest form for given fraction.

Complete step by step solution:
Here in the question they have given a fraction number that is $\dfrac{{18}}{{24}}$ and asking us to find the simplest form of it. Whenever the simplest form is asked first we need to find the common factor which is nothing but the number which divides both the numerator value and the denominator value with zero remainder. Here in this case the numerator value is nothing but the upper part of the fraction that is $18$ and the denominator value is nothing but the lower part of the fraction that is $24$ .
Therefore now we need to find the factor which divides the number $18$ and $24$ with zero remainder. As both $18$ and $24$ are even numbers we can divide these by $2$ which gives the result with zero remainder.
Therefore, we get
$\dfrac{{18}}{{24}} = \dfrac{{\left( {18 \div 2} \right)}}{{\left( {24 \div 2} \right)}}$
$ \Rightarrow \dfrac{{18}}{{24}} = \dfrac{9}{{12}}$
Now, we have to find common factors which divides the numbers $9$ and $12$ . The number $3$ divides both the number that is $9$ and $12$ with zero remainder.
Therefore, we get
$ \Rightarrow \dfrac{{18}}{{24}} = \dfrac{{\dfrac{9}{3}}}{{\dfrac{{12}}{3}}}$
On simplifying the above expression, we get
$ \Rightarrow \dfrac{{18}}{{24}} = \dfrac{3}{4}$
Now, we do not have any common factors which divides the numbers $3$ and $4$ except $1$, we can say that $\dfrac{3}{4}$ is the simplified form of $\dfrac{{18}}{{24}}$.

Note:
Here in this question they have directly given the fraction and asked us to write the simplest form or simplify the given value but sometimes they may give a decimal number or the percentage number and ask us to find the simplest fraction. Whenever finding the simplest fraction try to reduce as much as possible so that we get the correct answer.