Question

Fill in the place holders with the correct symbol $ > $ or $ < $ :
 $ \dfrac{3}{7}\,\square \,\dfrac{6}{7} $

Answer 1

Hint: The given question requires us to compare the two given fractions. We are given two fractions with the same denominator. So, we can compare both the fractions by first 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{3}{7} $ and $ \dfrac{6}{7} $ . So, we have to compare both the fractions.
Such fractions with equal denominators are called fractions. We can compare such fractions by directly comparing the numerators of fractions. Fractions with different unequal or different denominators are called unlike fractions. If we want to compare such fractions with different denominators, we first have to make the denominators equal by taking the least common multiple of the denominators of the fraction.
The fractions given to us have equal denominators. Hence, the fractions $ \dfrac{3}{7} $ and $ \dfrac{6}{7} $ are like fractions.
For comparing these fractions, we just have to compare the numerators.
The numerator of the fraction $ \dfrac{3}{7} $ is $ 3 $ and the numerator of $ \dfrac{6}{7} $ is $ 6 $ .
Now, we clearly know that $ 6 $ is greater than $ 3 $ .
Hence, comparing the original fractions, we get, $ \dfrac{6}{7} > \dfrac{3}{7} $ .
So, the correct answer is “$\dfrac{3}{7} < \dfrac{6}{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.