Question

Which fraction is bigger \[\dfrac{3}{4}\] or \[\dfrac{2}{3}\]?

Answer 1

Hint: We need to find the bigger fraction out of \[\dfrac{3}{4}\] and \[\dfrac{2}{3}\]. To find the bigger one, we need to compare the two fractions. To compare two fractions, we need to make their denominators equal. We will do this by taking the LCM of both the fraction and then the modified fractions with the same denominator will be equivalent to the given fractions. We will compare the numerator of the modified fractions and then the fraction with greater numerator will be the bigger fraction.

Complete step by step answer:
We need to check which one is bigger \[\dfrac{3}{4}\] or \[\dfrac{2}{3}\]. For that, we first need to make their denominators the same. Taking LCM of \[\dfrac{3}{4}\] or \[\dfrac{2}{3}\], we get
\[ \Rightarrow \dfrac{{3\left( 3 \right)or2\left( 4 \right)}}{{12}}\]
Multiplying the terms, we get
\[ \Rightarrow \dfrac{{9or8}}{{12}}\]
Splitting the denominator, we have
\[ \Rightarrow \dfrac{9}{{12}}or\dfrac{8}{{12}}\]
Here, \[\dfrac{3}{4}\] is equivalent to \[\dfrac{9}{{12}}\] and \[\dfrac{2}{3}\] is equivalent to \[\dfrac{8}{{12}}\].

Let’s compare \[\dfrac{9}{{12}}\] and \[\dfrac{8}{{12}}\]. We know, the fractions with the same denominator are compared through the numerator. The fraction for which the numerator is greater is bigger.
We know, \[9 > 8\].
Since both the fractions \[\dfrac{9}{{12}}\] and \[\dfrac{8}{{12}}\] have same denominator, and \[9 > 8\], we have
\[ \Rightarrow \dfrac{9}{{12}} > \dfrac{8}{{12}}\]
Now, since \[\dfrac{3}{4}\] is equivalent to \[\dfrac{9}{{12}}\] and \[\dfrac{2}{3}\] is equivalent to \[\dfrac{8}{{12}}\], we can write
\[ \Rightarrow \dfrac{9}{{12}} > \dfrac{8}{{12}}\]
\[ \therefore \dfrac{3}{4} > \dfrac{2}{3}\]

Hence, we get, \[\dfrac{3}{4}\] is bigger than \[\dfrac{2}{3}\].

Note: We can also solve this problem by making their numerators equal by multiplying and dividing both the fractions with numbers such that the resultant will give the same numerator for both the fractions. After making their numerators equal, out of these fractions different denominators, the one whose denominator is smaller than the other, the denominator of the other fraction is bigger.