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,

*
© Hozefa Arsiwala and teacherlookup.com, 2019-2020. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Hozefa Arsiwala and teacherlookup.com with appropriate and specific direction to the original content.
*