Question

Compare the following fractions and put an appropriate sign
a) \[\dfrac{3}{6}\square \dfrac{5}{6}\]
b) \[\dfrac{1}{7}\square \dfrac{1}{4}\]
c) \[\dfrac{4}{5}\square \dfrac{5}{5}\]
d) \[\dfrac{3}{5}\square \dfrac{3}{7}\]

Answer 1

Hint: In the given question we have to compare the given fractions. We know that the denominator part denotes the total number of parts number \[1\] is divided into and the numerator part gives us the value of the number of parts taken out of the total number of parts. Using this we can compare the given fractions.

Complete step-by-step answer:
We know that for the two fractions of the same denominator, if the numerator value of one fraction is less than the other, then the fraction with lesser value of numerator value is less than the fraction with greater value of numerator.
Now, in question a) and c) we can see that both the fractions to be compared have the same denominator. So, we compare them by their numerator value as given below,
In \[\dfrac{3}{6}\] and \[\dfrac{5}{6}\] we see that ,
\[
  3 < 5 \\
   \Rightarrow \dfrac{3}{6} < \dfrac{5}{6} \\
 \]
In \[\dfrac{4}{5}\] and\[\dfrac{5}{5}\],
\[
  4 < 5 \\
   \Rightarrow \dfrac{4}{5} < \dfrac{5}{5} \\
 \]
Same way if the numerator value is the same, we compare the fraction by seeing the denominator value.
If denominator value of one fraction is greater than other, then fraction value of that fraction is less than other. We see that in b) and d) numerator value is same, so we compare their fractions as,
In b),
\[
  7 > 4 \\
   \Rightarrow \dfrac{1}{7} < \dfrac{1}{4} \\
 \]
In d)
\[
  5 < 7 \\
   \Rightarrow \dfrac{3}{5} > \dfrac{3}{7} \\
 \]
Hence, we have solved the given problem.

Note: This is to note that when both the numerator and denominator value is different in the fractions to be compared it is not possible to compare them like above. We have to divide them most of the time to compare them except in some cases where we can compare them easily just by applying basic understanding of fractions.