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,