Question

Compare the fractions given below: $ \dfrac{4}{5} $ and $ \dfrac{5}{7} $ .

Answer 1

Hint: The given question requires us to compare the two given fractions. We are given two fractions with different denominators. So, we can compare both the fractions by making the denominators of the fraction equal by taking LCM of the denominators.

Complete step-by-step answer:
In the given question, we are provided with the fractions $ \dfrac{4}{5} $ and $ \dfrac{5}{7} $ . So, we have to compare both the fractions. The fractions given to us in the questions have different or unequal denominators.
For comparing the fractions, we convert them to like fractions having the same denominator.
The values of the denominator are not the same and so we take LCM for the denominator.
There is no common factor in between denominators $ 5 $ and $ 7 $ . LCM of the denominators $ 5 $ and $ 7 $ is $ 35 $ .
So, we have, $ \dfrac{4}{5} $ and $ \dfrac{5}{7} $ .
Now, we have to make the denominators of the fraction equal to the LCM by multiplying both the numerator and denominator of the fraction by the same number.
Hence, we multiply the numerator and denominator of $ \dfrac{4}{5} $ by $ 7 $ in order to make the denominator equal to $ 35 $ .
So, we get, \[\dfrac{4}{5} \times \dfrac{7}{7} = \dfrac{{28}}{{35}}\].
Also, we multiply the numerator and denominator of $ \dfrac{5}{7} $ by $ 5 $ in order to make the denominator equal to $ 35 $ .
So, we get, $ \dfrac{5}{7} \times \dfrac{5}{5} = \dfrac{{25}}{{35}} $ .
So, we have converted the fractions given to us into fractions having the same denominators. Now, we can compare the fractions \[\dfrac{{28}}{{35}}\] and \[\dfrac{{25}}{{35}}\] easily as the denominators of both the fractions are equal and we just have to compare the numerators.
So, \[\dfrac{{28}}{{35}} > \dfrac{{25}}{{35}}\].
Hence, comparing the original fraction, we get, $ \dfrac{4}{5} > \dfrac{5}{7} $
So, the correct answer is “ $ \dfrac{4}{5} > \dfrac{5}{7} $ ”.

Note: The given question deals with comparing the given fractional expressions. The problem can be solved by various methods. We can also directly compare the fractions by first converting them into decimal expressions. Care should be taken while carrying out the calculative steps