Lesson 5: Comparing Common Fractions

1. Comparing Fractions with the Same Denominators.
2. Comparing Fractions with Different Denominators.
3. Finding the Lowest Common Denominator.
4. Comparing Mixed Fractions.
5. Practice Game.

COMPARING FRACTIONS WITH THE SAME DENOMINATORS

It is easy to compare fractions if they have the same denominator. All you have to do is to compare their numerators.

If the two fractions have the same denominator, the larger fraction is the fraction with larger numerator.

Example1:

Which is larger,  or ?
 

    has only 2 fourth parts
 

    has 3 fourth parts

Since the dominators are the same, is larger than  , because 3 is larger then 2.
We write >

COMPARING FRACTIONS WITH DIFFERENT DENOMINATORS

To compare fractions with different denominators:

• make denominators the same using equivalent fractions
• compare the numerators

Example2:

Which is larger,  or ?
Since the fractions have different denominators, they cannot be compared until they have the same denominators. We can express both fractions as twelfths.
=   (the numerator and the denominator is multiplied by 4)
= .  (the numerator and the denominator is multiplied by 3)
Now it is easy to see that is larger then  ( >).
 

FINDING THE LOWEST COMMON DENOMINATOR

Sometimes finding the same denominator for both fraction is more complicated.

To find the lowest possible common denominator of 2 or more fractions:

1. Simplify the fractions if possible
2. Find the Lowest Common Denominator, which is the Lowest Common Multiple of all denominators.

Example3:

Which is smaller,  or ?

Looks difficult? Not so if we simplify both fractions:

=  (the numerator and the denominator is divided by 30)
= (the numerator and the denominator is divided by 3)

Now we have to compare and .
The Lowest Common Denominator (L.C.D.) for both fractions is the Lowest Common Multiple (L.C.M.) of 4 and 6.
The multiples of 6 are 6,12,....
12 is also a multiple of 4, so it is the L.C.D. for both fractions.

= (both the numerator and the denominator are multiplied by 3)

=  (both the numerator and the denominator are multiplied by 2)

< , so the smaller fraction is .

COMPARING MIXED FRACTIONS

When you know how to compare fractions, you know how to compare mixed fractions.

• The larger mixed fraction has the larger whole number part
• If both mixed fractions have the same whole number part, the larger mixed fraction
  has the larger fraction part.

Example4:

Write the mixed fractions 5, 4 and 4   in ascending order

5is the largest fraction, because it has the largest whole number part (5).
4 and  4have both the same whole number parts (4), so we have to compare fraction parts.
> (see example2), so  4> 4.

The ascending order is    4, 4,  5 .

descending order means from the largest to the smallest (or going down).
ascending order means from the  smallest to the largest (or going up).

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