Question

Compare the fractions and put an appropriate sign.
(i) \[\dfrac{3}{6}\boxed{}\dfrac{5}{6}\]
(ii) \[\dfrac{1}{7}\boxed{}\dfrac{1}{4}\]
(iii) \[\dfrac{4}{5}\boxed{}\dfrac{5}{5}\]

Answer 1

Hint: Here in this question, given a pair of some fraction we have to put an appropriate sign between each pair of fractions. Here we have to compare each pair of fractions and analyse the appropriate sign which represents the relation of two fractions either it will equal, lesser than, greater than etc.

Complete step by step solution:
A fraction is defined as a part of a whole or any number of equal parts. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
Comparing fractions means looking at two fractions and figuring out which one is lesser or greater.
Consider the given questions:

(i) \[\dfrac{3}{6}\boxed{}\dfrac{5}{6}\]
Since the denominator is the same, a fraction with a larger numerator is a larger number.
Therefore, \[\dfrac{3}{6} < \dfrac{5}{6}\].

(ii) \[\dfrac{1}{7}\boxed{}\dfrac{1}{4}\]
Here, the denominators of two fractions are different.
To identify the larger number, we have to cross multiply between the two fractions.
\[ \Rightarrow \,\,\dfrac{1}{7}\boxed{}\dfrac{1}{4}\]
On cross multiplying, we have
\[ \Rightarrow \,\,1 \times 4\,\boxed{}\,1 \times 7\]
\[ \Rightarrow \,\,4\,\boxed{}\,7\]
Along 4 and 7, 7 is the larger number i.e., \[4 < 7\]
Therefore, \[\dfrac{1}{7} < \dfrac{1}{4}\].

(iii) \[\dfrac{4}{5}\boxed{}\dfrac{5}{5}\]
Since the denominator is the same, a fraction with a larger numerator is the larger number.
Therefore, \[\dfrac{4}{5} < \dfrac{5}{5}\].

Note:
Remember, Like fractions can be compared easily as their denominator is the same but to compare unlike fraction. In like fractions the fraction which has a larger numerator is a greater fraction and in unlike fractions they should be converted to like-fractions by making the denominator same or by cross multiplication we can compare.