CLASS-5
COMPARISON OF FRACTION
Comparison Of Fractions -
Fractions can be compared by finding a common denominator and then comparing their numerators. The steps to compare two fractions are as follows:
- Find a common denominator: A common denominator is a multiple of both denominators. For example, if you want to compare 1/4 and 2/5, you can find a common denominator by multiplying 4 and 5 together to get 20.
- Convert the fractions to equivalent fractions with the common denominator: To do this, multiply both the numerator and denominator of each fraction by the same number so that the denominator becomes the common denominator. For example, to convert 1/4 to a fraction with a denominator of 20, multiply both the numerator and denominator by 5 to get 5/20. To convert 2/5 to a fraction with a denominator of 20, multiply both the numerator and denominator by 4 to get 8/20.
- Compare the numerators: Once both fractions have the same denominator, you can compare their numerators to determine which is larger. In this case, 8/20 is larger than 5/20, so 2/5 is greater than 1/4.
If the fractions have different signs, you may also need to consider their signs when comparing them. If both fractions are positive, the one with the larger numerator is greater. If one fraction is negative, the one with the smaller numerator is greater.
There are some comparing process of fractions are discussed below -
(a) Like denominators and unlike numerators :-
If two fractions have the same denominator, the fraction with greater numerator is greater than the fraction with the smaller numerator.
Fill in the blank using > or < sign to make correct statement:
33 27
-------, -------
50 50
33 27
------- > -------
50 50
[Since, (numerator 33) > (numerator 27)]
42 60 52
-------, -------, -------
29 29 29
60 52 42
------- > ------- > -------
29 29 29
[Since, (numerator 60) > (numerator 52) > (numerator 42)], OR
42 52 60
------- < ------- < -------
29 29 29
[Since, (numerator 42) < (numerator 52) < (numerator 60)]
(b) Like numerators and unlike denominators :-
If two fractions have the same numerator, the fraction with the smaller denominator is greater than the fraction with the greater denominator.
Fill in the blank using > or < sign to make correct statement:
5 5
-------, -------
14 8
5 5
------- < -------
14 8
[Since, (denominator 14) > (denominator 8)]
35 35 35
-------, --------, -------
23 45 76
35 35 35
------- > ------- > ------- , OR
23 45 76
[Since, (denominator 76) > (denominator 45) > (denominator 23)]
35 35 35
------- < ------- < -------
76 45 23
[Since, (denominator 76) > (denominator 45) > (denominator 23)]
(c) Unlike numerators and unlike denominators :-
First change all the given fractions into like fractions (same denominator) by taking the L.C.M. of the denominators and then compare.
8 5
Example.1) Compare between ------ and -------
9 6
8 5
Ans.) ------ and -------
9 6
L.C.M. = 2 × 3 × 3 = 18
8 8 × 2 16
------ = --------- = --------
9 9 × 2 18
5 5 × 3 15
-------- = ----------- = -------
6 6 × 3 18
16 15
------- > -------
18 18
(as 16 > 15)
8 5
So, ------- > -------- (Ans.)
9 6
11 12
Example.2) Compare 1 ------- and 1 --------
12 15
L.C.M. = 2 × 2 × 3 × 5 = 60
23 23 × 5 115
--------- = ------------ = -------
12 12 × 5 60
27 27 × 4 108
-------- = ----------- = --------
15 15 × 4 60
115 108
-------- > -------- (as 115 > 108)
60 60
23 27
------- > -------
12 15
11 12
1 ------- > 1 ------- (Ans.)
12 15