Yes, which fraction is larger or smaller? The question has great importance. As in many of the competitive exams, we are asked to arrange a set of given fractions. Before learning, how to compare the fractions, we'll learn the basics of fractions. Then we'll learn two methods, that will help us to tell "which fraction is larger".
Fraction: A number of the form `a/b` , where a and b are integers and b`!=` 0, is known as fraction. Here, a is called numerator and b is called denominator.
Example: `3/5` is a fraction, where Numerator = 3, and Denominator = 5.
7 is also a fraction, because it can be written as `7/1`
1st Method to find which fraction is larger
Method to compare two fractions: This method is known as Cross multiplication method. Steps are as follows:
Let `a/b` and `c/d` be the two given fractions, that we have to compare and decide which fraction is larger?
Find the product of numerator of the first fraction and the denominator of the 2nd fraction. So, we get ad and bc.
i) If ad > bc, then `a/b` > `c/d` .
ii) If ad = bc, then `a/b` = `c/d` .
iii) If ad < bc, then `a/b` < `c/d`
Ex: Compare, which fraction is larger `3/5` and `5/8`?
Products are 3X8= 24 and 5X5=25.
Here, 24 < 25, So `3/5`` < ``5/8`
Now, we can say very easily, which fraction is larger.
Hence, `5/8` is larger fraction among the two.
2nd Method to know which fraction is larger:
This method is used to compare more than two fractions:
Step I: Find the LCM or LCD of the given fractions. Let it be m.
Step II: Convert all the given fractions into like fractions, each having m as denominator.
Step III: Now we compare the numerators. The fraction having greater numerator is greater and vice- versa.
Ex: Arrange the fractions `2/5` , `3/10` and `9/14` in ascending order.
LCM of 5, 10 and 14 is 70.
Now, let us change each of the given fractions into an equivalent fraction having 70 as denominator.
Practice problems of which fraction is larger
1. Which fraction is larger: `5/6` or `6/7` ?
2. Which fraction is larger: `21/25` or `3/5` ?
Fraction: A number of the form `a/b` , where a and b are integers and b`!=` 0, is known as fraction. Here, a is called numerator and b is called denominator.
Example: `3/5` is a fraction, where Numerator = 3, and Denominator = 5.
7 is also a fraction, because it can be written as `7/1`
1st Method to find which fraction is larger
Method to compare two fractions: This method is known as Cross multiplication method. Steps are as follows:
Let `a/b` and `c/d` be the two given fractions, that we have to compare and decide which fraction is larger?
Find the product of numerator of the first fraction and the denominator of the 2nd fraction. So, we get ad and bc.
i) If ad > bc, then `a/b` > `c/d` .
ii) If ad = bc, then `a/b` = `c/d` .
iii) If ad < bc, then `a/b` < `c/d`
Ex: Compare, which fraction is larger `3/5` and `5/8`?
Products are 3X8= 24 and 5X5=25.
Here, 24 < 25, So `3/5`` < ``5/8`
Now, we can say very easily, which fraction is larger.
Hence, `5/8` is larger fraction among the two.
2nd Method to know which fraction is larger:
This method is used to compare more than two fractions:
Step I: Find the LCM or LCD of the given fractions. Let it be m.
Step II: Convert all the given fractions into like fractions, each having m as denominator.
Step III: Now we compare the numerators. The fraction having greater numerator is greater and vice- versa.
Ex: Arrange the fractions `2/5` , `3/10` and `9/14` in ascending order.
LCM of 5, 10 and 14 is 70.
Now, let us change each of the given fractions into an equivalent fraction having 70 as denominator.
Practice problems of which fraction is larger
1. Which fraction is larger: `5/6` or `6/7` ?
2. Which fraction is larger: `21/25` or `3/5` ?
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