Like and Unlike Fractions: Definition, Differences and Solved Examples

Like and unlike fractions are fundamental concepts in mathematics that describe fractions based on their denominators. Like fractions have the same denominator, which makes them easier to compare and perform operations on, while unlike fractions have different denominators and require conversion before calculations. Understanding these types of fractions is essential for working with fraction operations such as addition, subtraction, and comparison. In this guide, you will learn the definitions of like and unlike fractions, understand their key differences, and learn methods to compare and convert them.

Table of Contents

• What Are Like Fractions?
• What Are Unlike Fractions?
• Like Fractions vs Unlike Fractions
• How to Convert Unlike Fractions to Like Fractions
• Comparing Like and Unlike Fractions
• Arithmetic Operations on Like and Unlike Fractions
• Solved Examples on Like and Unlike Fractions
• Practice Problems on Like and Unlike Fractions

What Are Like Fractions?

Two or more fractions are called like fractions when their denominators are equal. For fractions p/q and r/s, they are like fractions if q = s.

Like fractions are fractions that have the same denominator. It doesn't matter what the numerators are as long as the bottom numbers are identical; the fractions are called ‘like fractions’.

Like Fractions Examples:

• 1/5 and 3/5: Both have denominator of 5  ⇒ Like fractions 

• 2/9, 5/9, and 8/9 ; All have denominator 9  ⇒ Like fractions 

• 7/11 and 4/11; both have denominator 11  ⇒ Like fractions 

• 1/4, 3/4, and 2/4; All have denominator 4  ⇒ Like fractions

What Are Unlike Fractions?

Two or more fractions are called unlike fractions when their denominators are not equal. For fractions p/q and r/s, they are unlike fractions if q ≠ s.

Unlike fractions are fractions that have different denominators.

Unlike Fractions Examples:

• 1/3 and 1/4: Denominators 3 and 4 are different. 

• 2/5 and 3/7: Denominators 5 and 7 are different. 

• 1/2, 3/5, and 4/9: All have different denominators. 

Like Fractions vs Unlike Fractions

How to Convert Unlike Fractions to Like Fractions

To convert unlike fractions into like fractions, find the LCM (Least Common Multiple) of their denominators and use it to make the denominators the same.

Steps to Convert Unlike Fractions to Like Fractions:

• Find the LCM of all the denominators.

• Convert each fraction so that its denominator equals the LCM (multiply both numerator and denominator by the same number).

• The resulting fractions are like fractions.

Example: Convert 1/3 and 1/4 to like fractions.

Step 1: Find the LCM of 3 and 4.

Multiples of 3: 3, 6, 9, 12, 15… Multiples of 4: 4, 8, 12, 16…

LCM = 12

Step 2: Convert each fraction to have a denominator of 12.

1/3: multiply numerator and denominator by 4; 1/3 = 4/12

1/4: multiply numerator and denominator by 3; 1/4 = 3/12

4/12 and 3/12 are like fractions equivalent to 1/3 and 1/4.

Comparing Like and Unlike Fractions

Comparing Like Fractions:

When fractions have the same denominator, just compare the numerators. The fraction with the larger numerator is greater.

Rule: If p/q and r/q are like fractions, then:

p/q > r/q if p > r

p/q < r/q if p < r

Example 1: Compare 5/9 and 7/9.

The denominator is the same: 9. So compare numerators: 5 < 7.

5/9 < 7/9

Comparing Unlike Fractions:

You can't directly compare unlike fractions because the pieces are of different sizes. First, you convert them to like fractions using the LCM and then compare numerators.

Method 1: LCM Method

Example: Compare 3/4 and 5/6.

Step 1: Find LCM of 4 and 6 = 12

Step 2: Convert:

3/4 = 9/12

5/6 = 10/12

Step 3: Compare: 9/12 < 10/12 ⇒ 3/4 < 5/6

Method 2: Cross-Multiplication Method (for two fractions)

For fractions p/q and r/s, cross-multiply:

If p × s > r × q, then p/q > r/s

If p × s < r × q, then p/q < r/s

Example: Compare 4/7 and 5/9.

4 × 9 = 36

5 × 7 = 35

36 > 35  ⇒ 4/7 > 5/9

Arithmetic Operations on Like and Unlike Fractions

• Addition of Like Fractions:

Rule: Keep the denominator the same and add the numerators.

(p/q) + (r/q) = (p + r) / q

Example: 3/8 + 2/8

= (3 + 2)/8

= 5/8

• Addition of Unlike Fractions:

Steps:

1. Find the LCM of the denominators.

2. Convert all fractions to like fractions using the LCM.

3. Add the numerators, keeping the common denominator.

4. Simplify if possible.

Example 1: 1/4 + 1/3

Step 1: LCM(4, 3) = 12

Step 2: 1/4 = 3/12 and 1/3 = 4/12

Step 3: 3/12 + 4/12 = 7/12

• Subtraction of Like Fractions:

Rule: Keep the denominator the same and subtract the numerators.

(p/q) − (r/q) = (p − r) / q

Example: 7/9 − 4/9

= (7 − 4)/9

= 3/9 = 1/3

• Subtraction of Unlike Fractions:

Steps:

1. Find the LCM of the denominators.

2. Convert to like fractions.

3. Subtract numerators, keeping the common denominator.

4. Simplify if needed.

Example 1: 3/4 − 1/3

Step 1: LCM(4, 3) = 12

Step 2: 3/4 = 9/12 and 1/3 = 4/12

Step 3: 9/12 − 4/12 = 5/12

• Multiplication of Fractions (Like and Unlike):

Multiplication is the same for both like and unlike fractions. Simply multiply the numerator × numerator and denominator × denominator.

(p/q) × (r/s) = (p × r) / (q × s)

Example 1: 3/5 × 4/7 = 12/35

Example 2: 2/3 × 6/8 = 12/24 = 1/2

• Division of Fractions (Like and Unlike):

To divide one fraction by another, multiply the first fraction by the reciprocal (flip) of the second.

(p/q) ÷ (r/s) = (p/q) × (s/r) = (p × s) / (q × r)

Example 1: (3/5) ÷ (2/7)

= (3/5) × (7/2)

= 21/10

Example 2: (5/8) ÷ (5/4)

= (5/8) × (4/5)

= 20/40

= 1/2

Solved Examples on Like and Unlike Fractions

Example 1: Check whether 5/12, 7/12, and 11/12 are like or unlike fractions.

Solution: Given 5/12, 7/12, and 11/12

All three have a denominator of 12. 

Therefore,  5/12, 7/12, and 11/12 are like fractions

Example 2: Simplify 4/15 + 7/15 − 2/15

Solution: Since all denominators are 15 (like fractions):

= (4 + 7 − 2)/15

= 9/15 = 3/5

Example 3: Add 2/3 and 3/5.

Solution: LCM(3, 5) = 15

2/3 = 10/15, and 3/5 = 9/15

10/15 + 9/15 = 19/15 = 1\frac{4}{15}

Example 4: Arrange the following in descending order: 3/5, 7/10, 2/5, 9/10.

Solution: 3/5 and 2/5 have the denominator 5; 7/10 and 9/10 have the denominator 10.

LCM(5, 10) = 10.

3/5 = 6/10

7/10 = 7/10

2/5 = 4/10

9/10 = 9/10

Arranging in descending order: 9/10 > 7/10 > 6/10 > 4/10

Therefore, 9/10 > 7/10 > 3/5 > ⅖

Example 5: Neha had 5/8 of a chocolate bar. She gave 1/4 of it to her brother. How much does she have left?

Solution: Amount of chocolate Neha had = 5/8

Amount of chocolate Neha gave to her brother = 1/4

Amount of chocolate remaining = 5/8 − 1/4

LCM(8, 4) = 8

1/4 = 2/8

5/8 − 2/8 = 3/8

Neha has 3/8 of the chocolate bar left.

Practice Problems on Like and Unlike Fractions

1. Identify whether the following are like or unlike fractions: 4/7 and 3/9.

2. Convert 1/2 and 2/3 into like fractions.

3. Add: 5/6 + 1/4

4. Subtract: 7/8 − 2/3

5. Compare 4/5 and 7/9 using cross-multiplication.

6. Arrange in ascending order: 1/2, 1/3, 1/4, 1/6.

7. Arrange 1/11, 8/11, 3/11, and 6/11 in ascending order.

8. Which is greater: 13/17 or 9/17?

9. Convert 2/5, 1/3, and 3/4 to like fractions.

10. Convert 4/5 and 9/2 to like fractions.