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Comparing Fractions

In comparing two fractions, we need to find which of the given fraction is greater or lesser than the other. Before learning how to compare fractions, we have to know what is a fraction.

A fraction is a number that can represented in the form of $\frac{a}{b}$ . where a is called as numerator and b is called as denominator. Earlier only reciprocals where represented as fractions. Numbers between two integers are represented as fraction. To compare two fraction we use less than symbol (<) and greater than symbol(>).

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How to compare Fractions

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Below are the solved examples on how to compare fractions -

Solved Examples

Question 1: Compare which are smaller fractions: $\frac{3}{11}$ or $\frac{6}{23}$ ?
Solution:
 
The LCD for the denominators 11, 23 is 253.

Calculate the fractions as $\frac{23*3}{253}$ and $\frac{11*6}{253}$ 

Now we get the solutions for the given fractions.

= $\frac{69}{253}$ and $\frac{66}{253}$ 

When comparing them  $\frac{6}{23}$ is smaller.

 

Correct answer is $\frac{6}{23}$ is smaller
Question 2: Compare which are smaller fractions:$\frac{11}{3}$ or $\frac{23}{7}$
Solution:
 
The LCD for the denominators 3, 7 is 21. 

Calculate the fractions as $\frac{7*11}{21}$ and $\frac{3*23}{21}$ 

Now we get the solutions for the given fractions.

= $\frac{77}{21}$ and $\frac{69}{21}$ 

When comparing them  $\frac{23}{7}$  is smaller. 

 

Correct answer is $\frac{23}{7}$ is smaller
Question 3: Compare which are smaller fractions: $\frac{21}{14}$ or $\frac{31}{16}$
Solution:
 
Convert the given fractions in to decimal form.

Calculate the fractions as $\frac{21}{14}$ and $\frac{31}{16}$ 

Now we get the solutions for the given fractions.

$\frac{21}{14}$=1.5 and $\frac{31}{16}$=1.9

When comparing them $\frac{21}{14}$ is smaller.

 

Correct answer is
Question 4: Compare which are greater fractions: $\frac{11}{13}$ or $\frac{21}{7}$
Solution:

The LCD for the denominator 13, 7 is 91.

Calculate the fractions as $\frac{7*11}{19}$ and $\frac{13*21}{91}$ 

Now we get the solutions for the given fractions.

$\frac{77}{91}$ and $\frac{273}{91}$ 

When comparing them $\frac{21}{7}$ is greater



Correct answer is $\frac{21}{7}$ is greater.
Question 5: Compare which are greater fractions: $\frac{13}{17}$ and $\frac{14}{3}$
Solution:
 

The LCD for the denominators 17, 3 is 51.


Calculate the fractions as  $\frac{3*13}{51}$ and $\frac{17*14}{15}$ 


Now we get the solutions for the given fractions.


= $\frac{39}{51}$ and $\frac{138}{51}$ 


When comparing them  $\frac{14}{3}$  is greater


 

Correct answer is $\frac{14}{3}$ is greater
Question 6:
Convert the given fractions in to decimal form.

Calculate the fractions as $\frac{26}{14}$ and $\frac{34}{15}$ 

Solution:
 
$\frac{26}{14}$=1.857 and $\frac{34}{15}$=2.266

When comparing them $\frac{34}{15}$ is greater
 

Correct answer is $\frac{34}{15}$ is greater
More topics in Compare Fractions
Equivalent Fractions
NCERT Solutions
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