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As we know, a fraction is made up of a numerator and a denominator. For example:  . Note that the denominator in a fraction is always non zero. We have also seen that fractions can be of different types such as proper, improper and mixed fractions.

 

Ordering and comparing fractions worksheet

 

Step 1: Before ordering and comparing fractions, make sure that the given set consists of all fractions. To do this you must convert any integers and mixed fractions to fractions.

 

Example:

Consider the given set:   .

You can write this set as: . In this example we have re-written the integer 1 and mixed number  as a fraction.

 

Step 2: We can now order and compare the fractions using the following rules:

 

When fractions have the same denominator

If all the fractions in the set have the same denominator, then you can directly compare the numerators and order the fractions.

 

Example:

Consider the given set: .

You can write this set as: 

Since all the three fractions have the same denominator, compare the numerators to determine the greater fraction.

Hence,    because the numerators 2 < 3 < 16.

 

Similarly, if you have negative fractions 

 

You can write this set as: 

As all fractions have the same denominator, now compare the numerators

Hence,   because the numerators -2 > -3 > -16.

 

When fractions have the same numerator

If all the fractions in the set have the same numerator, then you can directly compare the denominators and order the fractions. Note in this case the fraction that has the smaller denominator has the larger value.

 

Example:

Consider the given set: 

As all fractions have the same numerator, now compare the denominators.

Hence,    because the denominators 3 < 7 < 9.

 

When fractions do not have the same numerator or denominator

 

When the fractions do not have the same numerator or denominator, you can compare them by finding the Least Common Denominator.

 

Example:

Order the following fractions in ascending order:

 

Step 1: Since the fractions have unlike denominators, first find the Least Common multiple of the Denominators.

LCM of 3, 7, 5 = 3 x 7 x 2 = 42

 

Step 2: Using the least common denominator (LCD) write the fractions as equivalent fractions with like denominators.

 

Hence, the fractions can be written as

 

Step 3: You can now compare the fractions as they have the same denominators.

 

Therefore, 

 

Fractions in ascending order are 

 

Cross Multiplication

You can also use cross multiplication to compare two fractions.

Example:

Compare 

You can cross multiply the numerators with the denominators as shown below:

Therefore,

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