 How to Compare and Order Fractions? Maths Grade 5 | ORCHIDS |
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Comparing and Ordering Fractions

We can categorise all fractions into two types:

1. Like fractions: Fractions that have same denominators.
2. 2 / 7
,
5 / 7
,
6 / 7
,etc
3. Unlike fractions: Fractions that have different denominators.
4. 3 / 5
,
3 / 7
,
4 / 9
,etc

Comparison of fractions can be done in the following categories.

1. Comparing like fractions
2. Comparing unlike fractions
1. Comparing unlike fractions with same numerators
2. Comparing unlike fractions with different numerators
1. Comparing like fractions
2. Example 1: Let’s take an example of like fractions.

3 / 4
,
1 / 4
,→ Like fraction Compare the numerators.

3 > 1

So, Example 2:

6 / 12
,
11 / 12
,→ Like fraction Compare the numerators.

6 < 11

so,
6 / 12
is smaller than
11 / 12
. From the above example: 3. Comparing unlike fractions
1. Comparing unlike fractions with the same numerators

Example 1: Let’s take an example of unlike fractions with same numerator.

1 / 2
and
1 / 8 Compare the denominators.

2 < 8.

The fraction with the smaller denominator is the greater. So,  2. Comparing unlike fractions with different numerators

3. Example : Let’s take an example of unlike fractions with different numerator.

1 / 3
and
3 / 8 Here, we cannot predict which portion is larger and which one is smaller. Step 1: LCM of 3 and 8.

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ......

8 = 8, 16, 24, 32, .....

So, LCM of 3 and 8 is 24.

Step 2: Find equivalent fractions.

(Multiply numerator and denominator by the same number so that denominator will be 24.)

1 / 3
=
1 x 8 / 3 x 8
=
8 / 24

3 / 8
=
3 x 3 / 8 x 3
=
9 / 24 8 < 9

So,
8 / 24
<
9 / 24 So,
1 / 3
<
3 / 8 Ordering Fractions

• Ordering like fractions
• Example : Arrange the following fractions in Ascending order and descending order.

7 / 13
,
9 / 13
,
12 / 13

Ascending order:

• If denominators of the fractions are the same, arrange fractions according to ascending order of the numerators.
• The fraction which has the smallest numerator is the smallest fraction among all.
• So, ascending order of the fraction is:
5 / 13
,
7 / 13
,
9 / 13
,
12 / 13

Descending order:

• If denominators of the fractions are the same, arrange fractions according to descending order of the numerators.
• The fraction which has the biggest numerator is the biggest fraction among all.
• So, descending order of the fraction is:
12 / 13
,
9 / 13
,
7 / 13
,
5 / 13

• Ordering unlike fractions
• Case 1: Numerators are same.

Example : Arrange the following fractions in Ascending order and descending order.

17 / 3
,
17 / 11
,
17 / 9
,
17 / 15

Ascending order:

• If numerators of the fractions are same, arrange fractions according to descending order of the denominators.
• The fraction which has the biggest denominator is the smallest fraction among all.
• So, ascending order of the fraction is:
17 / 15
,
17 / 11
,
17 / 9
,
17 / 3

Descending order:

• If numerators of the fractions are the same, arrange fractions according to ascending order of the numerators.
• The fraction which has the smallest denominator is the biggest fraction among all.
So, descending order of the fraction is:
• 17 / 3
,
17 / 9
,
17 / 11
,
17 / 15

Case 2: Numerators are different.

Example : Arrange the following fractions in Ascending order and descending order.

3 / 4
,
1 / 2
,
7 / 12
,
4 / 6

Step 1:Find the LCM of denominators.

Step 2:Make all denominators equal to LCM. It will convert all fractions into like fractions.

Step 3:By using like fractions comparison rule, ordered the fractions.

LCM of 4, 2, 12, 6 = 12

3 / 4
=
3 x 3 / 4 x 3
=
9 / 12

1 / 2
=
1 x6 / 2 x 6
=
6 / 12

7 / 12
(Keep it as it is)
4 / 6
=
4 x 2 / 6 x 2
=
8 / 12

Now, we have new fractions:
9 / 12
,
6 / 12
,
7 / 12
,
8 / 12

Ascending order:
6 / 12
,
7 / 12
,
8 / 12
,
9 / 12
=
1 / 2
,
7 / 12
,
4 / 6
,
3 / 4
(Original fractions are equivalent to new fractions)
Descending order:
3 / 4
,
4 / 6
,
7 / 12
,
1 / 2

Comparing and ordering fractions on a number line

Number line: A number line is a straight line on which the numbers are placed at equal distances. How to write the fractions on a number line?

1. Write the proper fractions on a number line:
• Step 1:Divide the interval from 0 to 1 into equal parts as equal to the denominator.
• Step 2:Count the number of intervals from 0 as equal to the numerator. And make a mark.
• Example

Write the fraction
4 / 5
on the number line.

Step 1:Divide the interval from 0 to 1 into 5 equal parts.

Step 2:Count 4 intervals from 0 and make a mark at the 4th interval.

The fraction
4 / 5
on a number line: 2. Write the improper fractions on a number line:
• Step 1:Convert the improper fraction into a proper fraction.
• Step 2:Divide each interval into equal parts as many as the denominator.
• Step 3:Count the number of intervals as equal to the numerator after the whole number of the mixed fraction.
• Example

Write the fraction
5 / 3
on the number line.

Step 1:Convert the improper fraction 5/3 into a proper fraction. 5 / 3
=1
2 / 3

Step 2:Denominator = 3

Divide each interval into 3 equal parts.

Step 3:Numerator = 2, whole number in mixed fraction = 1

Count 2 intervals after 1.

The fraction 1
2 / 3
=
5 / 3
on a number line: In this way, we can write any fraction on a number line.

How to compare and order the fractions by a number line?

• Step 1: Make all the fractions like fractions.
• Step 2: Write all the fractions on a number line.
• Step 3: From left to right, all fractions are getting arranged in ascending order on a number line. Now compare all fractions.
• Example

Compare the following fractions by using a number line and order them in ascending and descending order.

1 / 2
,
7 / 3
,
5 / 6

Step 1: Make all the fractions like fractions.

1 x 3 / 2 x 3
=
3 / 6

7 x 2 / 3 x 2
=
14 / 6 7 / 3
= 2
2 / 6

Step 2:Write all the following fractions on a number line -

3 / 6
=
1 / 2
, 2
2 / 6
=
7 / 3
,
5 / 6 Step 3:From left to right, all fractions are getting arranged in ascending order on a number line.

So, the ascending order of the fraction:
1 / 2
,
5 / 6
,
7 / 3

The descending order of the fraction:
7 / 3
,
5 / 6
,
1 / 2

Misconception:

Don’t be confused while comparing fractions with the same numerator.

Example: In the above example, numerators are same in both the fractions. Although the denominator of the first fraction is larger, that fraction is smaller. So, be careful when comparing fractions with equal numerators.

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