Question

How do you write \[\dfrac{{16}}{{24}}\] in simplest form?

Answer 1

Hint: Here, we will first find the factor of the numbers present in the numerator and denominator. Using the factors, we will find the HCF of both the numbers. Then, we will divide the numerator and the denominator by their highest common factor such that we get the simplest form of the fraction.

Complete step by step solution:
In order to write the given fraction \[\dfrac{{16}}{{24}}\] in the simplest form,
We will try to reduce this by finding the HCF of the numerator and the denominator.
Hence, we can write them as:
\[16 = 2 \times 2 \times 2 \times 2 = {2^4}\]
\[24 = 2 \times 2 \times 2 \times 3 = {2^3} \times 3\]
Therefore, the highest common factor, HCF of 16 and 24 \[ = 2 \times 2 \times 2 = 8\]
Now, we will divide the numerator and the denominator by 8. Therefore, we get
\[ \Rightarrow \dfrac{{16}}{{24}} = \dfrac{{\dfrac{{16}}{8}}}{{\dfrac{{24}}{8}}} = \dfrac{2}{3}\]
As we can see that the numerator is smaller than the denominator.
Thus, this is a proper fraction.

Hence, we can write \[\dfrac{{16}}{{24}}\] in simplest form as \[\dfrac{2}{3}\].

Note:
Since, in the simplest form, we get a proper fraction. Hence, we should know that a proper fraction is a fraction in which the numerator is less than the denominator. Also, we could have obtained the simplest form as a mixed fraction which is a number that contains both the whole number and the proper fraction. An improper fraction is a fraction where the numerator is greater than the denominator hence, it is called an ‘improper’ fraction. When we convert a mixed fraction into an improper fraction or vice-versa, their values remain the same and only the way of writing those numbers is different.