When you need to compare two Unlike Fractions, whose numerators are different, First; find equivalent
fractions of both the given unlike fractions with a common denominator. Then compare equivalent fractions and the fraction
with larger numerator is the biggest and vice-verse.
Remember - Two important following point
1). Common denominator must be a multiple of denominator of both given unlike fractions.
2). Common denominator should be as small as possible, as it is easier to do further calculations.
That's Why, always find a common denominator with the help of LCM for given unlike fractions
Following are few examples explaining How to compare fractions with different numerator and find whether a fraction is greater or smaller :-
Example 1 : Compare the following fractions and find which one is greater
Answer = The given unlike fractions have different numerators i.e 1 and 2,
So, first find a common denominator with the help of LCM. i.e find LCM of 3 and 5 and we get;
LCM of 3 and 5 = 15.
Now, find equivalent fractions with common denominator(15) of given unlike fraction;
Equivalent Fraction will be
1
3 | = | (1 x 5)
(3 x 5) | = | 5
15 |
2
5 | = | (2 x 3)
(5 x 3) | = | 6
15 |
| Now compare | 5
15 | and | 6
15 |
As numerator 6 is larger than numerator 5 of given fractions,
| or corresponding fractions | 2
5 | > | 1
3 |
Example 2 : Compare the following fractions and find which one is greater
Answer = The given unlike fractions have different numerators i.e 7 and 1,
So, first find a common denominator with the help of LCM i.e find LCM of 6 and 15 and we get;
LCM of 6 and 15 = 30
Now, find equivalent fractions with common denominator(30) of given unlike fraction;
Equivalent Fraction will be
7
6 | = | (7 x 5)
(6 x 5) | = | 35
30 |
1
15 | = | (1 x 2)
(15 x 2) | =2
30 |
| Now compare | 35
30 | and | 2
30 |
As numerator 35 is larger than numerator 2 of given fractions,
| or corresponding fractions | 7
6 | > | 1
15 |
Example 3 : Compare the following fractions and find which one is greater
Answer = The given unlike fractions have different numerators i.e 7 and 4,
So, first find a common denominator with the help of LCM i.e find LCM of 10 and 4 and we get;
LCM of 10 and 4 = 20.
Now, find equivalent fractions with common denominator(20) of given unlike fraction
Equivalent Fraction will be
7
10 | = | (7 x 2)
(10 x 2) | = | 14
20 |
3
4 | = | (3 x 5)
(4 x 5) | = | 15
20 |
| Now compare | 14
20 | and | 15
20 |
As numerator 15 is larger than numerator 14 of given fractions,
| or corresponding fractions | 3
4 | > | 7
10 |
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