Question

Fill in the boxes with the correct symbol \[0, > , < {\text{ or = }}\]
 $ \dfrac{8}{8} $ ……………... $ \dfrac{2}{2} $

Answer 1

Hint: Here we are given two fractions and we have to compare whether they are less than, greater than or equal to each other. Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from the certain size. First of all simplify the fraction and then compare.

Complete step-by-step answer:
Take the two given fractions one by one –
 \[\dfrac{8}{8}\]
Common multiple from the numerator and the denominator cancel each other. Therefore here remove from the numerator and the denominator.
 \[\dfrac{8}{8} = 1\] .... (A)
Now let's consider,
 $ \dfrac{2}{2} $
Common multiple from the numerator and the denominator cancel each other. Therefore here remove from the numerator and the denominator.
 \[\dfrac{2}{2} = 1\] .... (B)
From the equations (A) and (B), we can observe that both the fraction’s resultant values are equal.
Hence,
  $ \dfrac{8}{8} = \dfrac{2}{2} $
So, the correct answer is “=”.

Note: In the questions of comparison, always convert the given integers and fractions in the simplified form. Here we got the resultant value of the fraction as the natural number but in case simplified form is also the fraction then convert both the fraction in the form of equivalent fraction in such a way that the denominator of both the fraction are same and equal.
For Example to compare- $ \dfrac{2}{3} $ and $ \dfrac{6}{4} $
Here, $ \dfrac{2}{3} $ is the simplified form.
 $ \dfrac{6}{4} = \dfrac{3}{2} $ (Removed common multiple )
Now, we have to compare –
 $ \dfrac{2}{3} $ and $ \dfrac{3}{2} $
Multiply both the fraction with
 $
   \Rightarrow \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{4}{6}{\text{ }}....{\text{ (i)}} \\
   \Rightarrow \dfrac{3}{2} \times \dfrac{3}{3} = \dfrac{9}{6}{\text{ }}....{\text{ (ii)}} \\
  $
By observing above two equations (i) and (ii), we can say that the fraction (ii) is greater than (i)
 $
   \Rightarrow \dfrac{4}{6} < \dfrac{9}{6} \\
   \Rightarrow \dfrac{2}{3} < \dfrac{3}{2} \\
  $