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Comparing Fractions

A fraction consists of two numbers divided by a line or slash, in which the top number (or numerator) represents the quantity of how many fractional parts are there out of the denominator, wherein the denominator of a fraction represents the number, into how many parts that the object was divided into.

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How to Compare Fractions?

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Comparing Fractions with the Same Denominator:
If the denominators of two or more fractions are same, then, the fraction with the largest numerator is the larger or largest fraction.

Comparing Fractions with the Different Denominator (Unlike Fractions):

Method 1: Making Equivalent Fractions:

If the denominators of two or more fractions are not same, then first, we have to find the common denominator of all the fractions, secondly, we will make equivalent fractions with the new denominator, wherein, we multiply the numerator and the denominator of any one fraction by the same number, so that both the fractions would have the same denominator and finally we will compare the fraction with the largest numerator which will be the larger or largest fraction.

Method 2: Cross Multiplication Method:

The other method is of cross multiplication in which, we multiply the numerator of the first fraction by the denominator of the second fraction and we note the answer got, and then we multiply the numerator of the second fraction by the denominator of the first fraction and again note down the answer.
On comparing the answers, the number which is greater will represent the greatest fraction of them all and vice versa.

The similar process would be repeated to make a comparison of more than two fractions, where we first cross multiply the two fractions, and the resulting fraction would be cross multiplied by the third fraction and so on

Solved Examples

Question 1: Compare $\frac{5}{8}$ and $\frac{3}{8}$.
Solution:
 
$\frac{5}{8}$ is larger than $\frac{3}{8}$ because they have the same denominator and we just have to look out for the largest numerator, which is 5, Hence, $\frac{5}{8}$ is greater than $\frac{3}{8}$.
 

Question 2: Compare $\frac{5}{12}$ and $\frac{1}{3}$.
Solution:
 
As this is the case of unlike fractions, so to make them equivalent, $\frac{1}{3}$ would be multiplied by $\frac{4}{4}$. After the multiplication ($\frac{1}{3}$ * $\frac{4}{4}$ = $\frac{4}{12}$), the comparison can be made between $\frac{5}{12}$ and $\frac{4}{12}$.
Hence, $\frac{5}{12}$ is greater than $\frac{4}{12}$.
 

Question 3: Compare $\frac{2}{3}$ and $\frac{3}{4}$.
Solution:
 
This is the case of unlike fractions, so we will multiply $\frac{2}{3}$ by $\frac{4}{4}$ which gives $\frac{8}{12}$ and multiply $\frac{3}{4}$ by $\frac{3}{3}$ which gives $\frac{9}{12}$.
On comparing, $\frac{9}{12}$ is larger than $\frac{8}{12}$.
Hence, $\frac{3}{4}$ is greater than $\frac{2}{3}$.
 

Question 4: Compare $\frac{3}{5}$, $\frac{5}{9}$ and $\frac{6}{11}$.
Solution:
 
On applying the method of cross multiplication, we will first multiply, 3 * 9 and 5 * 5, which is 27 and 25, so 27 is greater than 25, so $\frac{3}{5}$ is greater than $\frac{5}{9}$.

Now comparing $\frac{3}{5}$ and $\frac{6}{11}$, we multiply 3 * 11 and 5 * 6 which is 33 and 30, here 33 is greater, this implies $\frac{3}{5}$ is greater than $\frac{6}{11}$.
Now comparing $\frac{5}{9}$ and $\frac{6}{11}$, 5 * 11 = 55 and 6 * 9 = 54, that is $\frac{5}{9}$ is greater than $\frac{6}{11}$.
Hence, $\frac{3}{5}$ > $\frac{5}{9}$ > $\frac{6}{11}$.
 


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