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Ordering Fractions

A group of fractions can be ordered in ascending order that is from least fraction to the greatest fraction. The fractions can only be compared if the numerator or denominator of all the fractions are same. If they are not same, then we make the denominators of all fractions same by finding the lowest common denominator.

1) When numerators are same: If numerators are same, we use denominators to order fractions. The fraction with greater denominator is smaller.

For example: $\frac{5}{6}$ and $\frac{5}{8}$ .

$\frac{5}{8}$ < $\frac{5}{6}$ .

2) When denominators are same: In this case we use numerators to order fractions. Fraction with smaller numerator is smaller.

Like in $\frac{4}{5}$ and $\frac{2}{5}$

$\frac{2}{5}$ < $\frac{4}{5}$.

3) When both numerators and denominators are different: LCM (lowest common multiple ) of denominators is found. Fractions are renamed to have same denominators. Once the denominators are same, the fractions can be arranged as per the numerators.

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Compare and Order Fractions

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The explanations for compare and order fractions are as follows,

Order fractions:

Many of the rules to be followed by the fraction for the purpose of ordering the fractions. They are shown below,

  • The least common factor must be found out for the ordering purpose.

  • The arrangements are made for the ordering purpose. It can be either in the form of ascending or in the form of descending order.

  • After finding all these we can easily order the fractions.


Compare fractions:

Many of the rules to be followed by the fraction for the purpose of comparing the fractions. They are shown below,

  • Make the denominator should be equal for all the fractions that are given.

  • Then compare the top terms present in the given fractions. The signs are also included in the comparing fractions.

  • After finding all these we can easily compare the fractions.

How to Order Fractions

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Solved Examples

Question 1: What is the order of the given fraction, `3/4` , `2/4` , `13/4` , `12/4` , `6/4` , `8/4` , `26/4` .
Solution:
 
Step 1: The given fractions are,

`3/4` , `2/4` , `13/4` , `12/4` , `6/4` , `8/4` , `26/4`

Step 2: The bottom terms are equal for all the fractions, we are now ordering the numerator terms, we get,

2 < 3 < 6 < 8 < 12 < 13 < 16 < 26

Step 3: Now write the ascending order for the given fractions, we get,

`2/4` , `3/4` , `6/4` , `8/4` , `12/4` , `13/4` , `26/4` .

This is called the ordering of fractions in ascending order.

Step 4: Now write the descending order for the given fractions, we get,

$\frac{26}{4}$, $\frac{13}{4}$, $\frac{12}{4}$, $\frac{8}{4}$, $\frac{6}{4}$, $\frac{3}{4}$, $\frac{2}{4}$ .

This is called the ordering of fractions in descending order.
 

Question 2: What is the order of the given fraction, `35/23` , `65/23`.
Solution:
 
Step 1: The given fraction to compare are,

`35/23` , `65/23`

Step 2: The bottom terms are equal to all the fractions, we are now comparing the numerator terms, we get,

65 > 35

Step 3: Now write the comparing order for the given fractions, we get,

`65/23` > `35/23`

This is called the comparing of fractions.
 


Order Fractions from Least to Greatest

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Below you could see the examples for order fractions from least to greatest

Solved Examples

Question 1: Order the following fractions from least to greatest: $\frac{5}{8}$ , $\frac{5}{9}$ , $\frac{5}{2}$ , $\frac{5}{4}$ , $\frac{5}{11}$ .
Solution:
When numerators are same, we use denominators to order. Fraction with lower denominator is greater.

So the correct ordering is: $\frac{5}{2}$ , $\frac{5}{4}$ , $\frac{5}{8}$ , $\frac{5}{9}$ and $\frac{5}{11}$ 

Question 2: Order the following fractions from least to greatest: $\frac{3}{11}$ , $\frac{1}{11}$ , $\frac{5}{11}$ , $\frac{10}{11}$ , $\frac{7}{11}$.
Solution:
When the denominators are same, we order fractions using numerators. The fraction with greater numerator is greater.

So the correct ordering is : $\frac{1}{11}$ , $\frac{3}{11}$ , $\frac{5}{11}$ , $\frac{7}{11}$ and $\frac{10}{11}$ 

Ordering Fractions Practice

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Practice Problems

Question 1: What is the order of the given fraction, `13/5` , `12/5` , `15/5` , `14/5` , `16/5` , `19/5` , `17/5`
Question 2: What is the order of the given fraction, `65/34`, `67/34`.
More topics in Ordering Fractions
Ordering Fractions with Unlike Denominators
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