Like Fractions and Unlike Fractions

Like Fractions and Unlike Fractions are two types of fractions that differ based on their denominators.

• Like Fractions are fractions that have the same denominator.

• Unlike Fractions are fractions that have different denominators.

Understanding the difference between like and unlike fractions is important because arithmetic operations such as addition and subtraction of fractions are easier when the fractions are like. Unlike fractions need to be converted into like fractions before performing these operations.

What Are Like Fractions?

Definition of Like Fractions -Like fractions are fractions that have the same denominator. This means the whole has been divided into the same number of equal parts in each fraction. Since the denominators are the same, like fractions are easy to compare and combine using addition or subtraction. You only need to work with the numerators.

Examples of Like Fractions:

• 3/8, 5/8, and 7/8 — same denominator (8)

• 1/10 and 9/10 — same denominator (10)

Also read: Numerator and Denominator

What Are Unlike Fractions?

Definition of Unlike Fration - Unlike fractions are fractions that have different denominators. Each fraction divides the whole into a different number of equal parts, so you cannot directly add, subtract, or compare them until the denominators are the same. Unlike fractions must be converted into like fractions before performing arithmetic operations. 

Examples of Unlike Fractions:

• 1/2 and 1/3 — different denominators (2 and 3)

• 2/5 and 3/10 — different denominators (5 and 10)

Because their denominators are different, working with unlike fractions requires an extra step, usually finding the least common denominator (LCM).

Also read: Adding Fractions

Comparing Like Fractions and Unlike Fractions

There are different ways to compare fractions depending on whether they are like fractions or unlike fractions. Let’s understand each case with simple explanations and new examples.

Comparing Like Fractions

Like fractions have the same denominator. So, when comparing like fractions, we only need to compare the numerators. The fraction with the larger numerator is greater.

Example: Compare 3/7 and 5/7

Both have the same denominator (7), so we compare the numerators.

5 is greater than 3.

Therefore, 3/7 < 5/7

Comparing Unlike Fractions

Unlike fractions have different denominators, so we can’t directly compare them. There are two common cases:

Case 1: Same Numerators, Different Denominators

When comparing unlike fractions with the same numerators, the fraction with the smaller denominator is larger. That’s because each part is larger when divided into fewer pieces.

Example: Compare 4/9 and 4/11

Both have the same numerator (4)

Compare the denominators 9 < 11

So, 4 parts out of 9 are larger than 4 parts out of 11.

Therefore,  4/9 > 4/11

Case 2: Different Numerators and Different Denominators

When both numerators and denominators are different, we first convert the fractions into like fractions (with the same denominator) by using the LCM of the denominators. Then we compare the resulting numerators.

Example: Compare 3/4 and 5/6

Step 1: LCM of 4 and 6 = 12

Step 2: Convert 3/4

3 × 3 = 9, 4 × 3 = 12 →9/12 or 3/4

Convert 5/6

5 × 2 = 10, 6 × 2 = 12 → 10/12 or 5/6

Step 3: Compare the two like fractions:

 9/12 < 10/12

Therefore, , 3/4 < 5/6

Also read:  Unit fractions

Arithmetic Operations on Like Fractions and Unlike Fractions

There are four basic arithmetic operations that can be performed on like and unlike fractions:

1. Addition

2. Subtraction

3. Multiplication

4. Division

Whether a fraction is like (same denominator) or unlike (different denominators), the method used to solve it will differ. Let’s explore each operation in detail.

Addition of Like and Unlike Fractions

We can simply add two or more like fractions by adding the numerators and keeping the denominators the same.

Example: Add: 5/8 + 2/8

Step 1: Add numerators: 5 + 2 = 7

Sep 2: Keep denominator: 8

5/8 + 2/8 = 7/8

For adding two unlike fractions, we first convert them to like fractions by finding the LCM of the denominators, and then add the resulting like fractions.

Example:  Add 3/5 + 4/7

Step 1: Find LCM of 5 and 7 = 35

Step 2: Convert to like fractions:

3/5 = (3 × 7)/(5 × 7) = 21/35

4/7 = (4 × 5)/(7 × 5) = 20/35

Step 3: Add:

21/35 + 20/35 = 41/35 or 1 6/35 

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Subtraction of Like and Unlike Fractions

We can simply subtract two or more like fractions by subtracting the numerators and keeping the denominators the same.

Example: Subtract 7/9 − 4/9

Step 1: Subtract numerators: 7 − 4 = 3

Step 2: Keep denominator: 9

Answer: 7/9 − 4/9  = 3/9 or 1/3

For subtracting two unlike fractions, we first convert them to like fractions by finding the LCM of the denominators, and then subtract.

Example: Subtract 2/5 from 5/7

Step 1: LCM of 5 and 7 = 35

Step 2: Convert to like fractions:
5/7 = (5 × 5)/(7 × 5) = 25/35

2/5 = (2 × 7)/(5 × 7) = 14/35

Step 3: Subtract:

25/35 − 14/35 = 11/35

Answer:  5/7 - 2/5 = 11/35

Also read : Greatest Common Factor

Multiplication of Like and Unlike Fractions

For multiplying any two fractions (like or unlike), we:

Step 1: Multiply the numerators

Step 2: Multiply the denominators

Step 3: Simplify the result, if possible

Example:  Multiply 3/10 × 4/10

Step 1: Multiply numerators: 3 × 4 = 12

Step 2: Multiply denominators: 10 × 10 = 100

Answer: 3/10 × 4/10  = 12/100 or  3/25

Example 2:  Multiply 2/3 × 5/7

Step 1: Multiply numerators: 2 × 5 = 10

Step 2: Multiply denominators: 3 × 7 = 21

Answer:  2/3 × 5/7 = 10/21

Also read: Multiple of fractions 

Division of Like and Unlike Fractions

To divide a fraction by another fraction (like or unlike), follow these steps:

Step 1: Flip the second fraction (take its reciprocal)

Step 2: Change division (÷) to multiplication (×)

Step 3: Multiply as usual

Step 4: Simplify the result

Example:  Divide 4/9 ÷ 2/9

Step 1: Flip second fraction

2/9 becomes 9/2

Step 2: Multiply

4/9 × 9/2 = (4 × 9) / (9 × 2) 

Answer: 4/9 ÷ 2/9 = 36 / 18 or   2

Example 2: Divide  3/5 ÷ 2/7

Step 1: Flip second fraction

 2/7 becomes 7/2

Step 2: Multiply 3/5 × 7/2 

= (3 × 7)/(5 × 2)  = 21/10 

Answer: 3/5 ÷ 2/7 = 21/10 

Also read: Zero divided by a number

Like and Unlike Fractions Examples

Example 1: Which of the following pairs are like fractions?

A. 5/6 and 2/6
B. 3/8 and 3/9
C. 1/4 and 7/4
D. 2/3 and 4/5

Solution: 

A and C are like fractions (same denominator).

B and D are unlike fractions (different denominators).

Example 2: Explain why 6/7 and 6/10 are unlike fractions, even though the numerators are the same.

Solution: 

Although both fractions have the same numerator (6), their denominators are different (7 and 10). The number of parts the whole is divided into is not the same. Therefore, 6/7 and 6/10 are unlike fractions.

Also read:  Division of Fractions 

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