Like and Unlike Fractions
You already know that fractions have a top number (numerator) and a bottom number (denominator). When two fractions have the same denominator, they are called like fractions. When they have different denominators, they are called unlike fractions.
Knowing the difference between like and unlike fractions is important because adding, subtracting, and comparing fractions is much easier when the denominators are the same.
In Class 6 NCERT Maths, you will learn to tell like fractions from unlike fractions and how to convert unlike fractions to like fractions.
What is Like and Unlike Fractions - Grade 6 Maths (Fractions)?
Definition:
- Like fractions are fractions that have the same denominator. Examples: 1/5, 2/5, 3/5, 4/5.
- Unlike fractions are fractions that have different denominators. Examples: 1/3, 2/5, 3/7.
In like fractions, the parts are the same size (fifths with fifths, eighths with eighths). In unlike fractions, the parts are different sizes, so you cannot compare or add them directly.
Like and Unlike Fractions Formula
How to convert unlike fractions to like fractions:
- Find the LCM (Least Common Multiple) of the denominators.
- Convert each fraction to an equivalent fraction with the LCM as the new denominator.
New numerator = (LCM / old denominator) x old numerator
Example: Convert 1/3 and 1/4 to like fractions.
- LCM of 3 and 4 = 12
- 1/3 = (12/3 x 1)/12 = 4/12
- 1/4 = (12/4 x 1)/12 = 3/12
- Now 4/12 and 3/12 are like fractions.
Types and Properties
Quick comparison:
- Like fractions: Same denominator. Easy to compare — just compare numerators. Larger numerator = larger fraction.
- Unlike fractions: Different denominators. Must convert to like fractions first, then compare.
Examples of like fractions:
- 2/7, 5/7, 1/7, 6/7 (all have denominator 7)
- 3/10, 7/10, 1/10 (all have denominator 10)
Examples of unlike fractions:
- 1/2, 1/3, 1/4 (denominators 2, 3, 4 are all different)
- 3/5, 2/7, 5/9 (denominators 5, 7, 9 are all different)
Solved Examples
Example 1: Identifying Like Fractions
Problem: Which of the following are like fractions? 3/8, 5/8, 2/5, 7/8, 1/3.
Solution:
Like fractions have the same denominator.
3/8, 5/8, and 7/8 all have denominator 8.
Answer: 3/8, 5/8, and 7/8 are like fractions.
Example 2: Identifying Unlike Fractions
Problem: Are 2/3 and 4/5 like or unlike fractions?
Solution:
The denominators are 3 and 5. They are different.
Answer: 2/3 and 4/5 are unlike fractions.
Example 3: Converting Unlike to Like Fractions
Problem: Convert 2/3 and 3/4 to like fractions.
Solution:
Step 1: LCM of 3 and 4 = 12.
Step 2: 2/3 = (2 x 4)/(3 x 4) = 8/12
Step 3: 3/4 = (3 x 3)/(4 x 3) = 9/12
Answer: The like fractions are 8/12 and 9/12.
Example 4: Comparing Like Fractions
Problem: Which is greater: 5/9 or 7/9?
Solution:
Both fractions have the same denominator (9). Compare the numerators.
7 > 5, so 7/9 > 5/9.
Answer: 7/9 is greater.
Example 5: Comparing Unlike Fractions
Problem: Which is greater: 3/4 or 5/6?
Solution:
Step 1: LCM of 4 and 6 = 12.
Step 2: 3/4 = 9/12 and 5/6 = 10/12.
Step 3: Compare: 10/12 > 9/12.
Answer: 5/6 is greater.
Example 6: Converting Three Fractions to Like Fractions
Problem: Convert 1/2, 2/3, and 3/4 to like fractions.
Solution:
Step 1: LCM of 2, 3, and 4 = 12.
Step 2:
- 1/2 = 6/12
- 2/3 = 8/12
- 3/4 = 9/12
Answer: The like fractions are 6/12, 8/12, and 9/12.
Example 7: Arranging Like Fractions in Order
Problem: Arrange in ascending order: 7/11, 3/11, 9/11, 1/11.
Solution:
All have the same denominator (11). Just compare numerators: 1 < 3 < 7 < 9.
Answer: 1/11, 3/11, 7/11, 9/11.
Example 8: Arranging Unlike Fractions in Order
Problem: Arrange in ascending order: 1/2, 1/3, 1/6.
Solution:
Step 1: LCM of 2, 3, 6 = 6.
Step 2: 1/2 = 3/6, 1/3 = 2/6, 1/6 = 1/6.
Step 3: Order: 1/6 < 2/6 < 3/6.
Answer: 1/6, 1/3, 1/2.
Real-World Applications
Why this matters:
- Adding fractions: You can only add like fractions directly. To add unlike fractions, first convert them to like fractions.
- Comparing portions: When comparing slices of pizza — if one person eats 2/5 and another eats 3/8, you need like fractions to compare.
- Cooking: Recipes use different fractions (1/2 cup, 1/3 cup). Converting to like fractions helps combine them.
- Sharing equally: When dividing things among groups of different sizes, unlike fractions arise naturally.
Key Points to Remember
- Like fractions have the same denominator.
- Unlike fractions have different denominators.
- To compare or add unlike fractions, convert them to like fractions first.
- To convert: find the LCM of the denominators and make equivalent fractions.
- For like fractions, the fraction with the larger numerator is greater.
- Like fractions are easier to work with than unlike fractions.
- Every set of unlike fractions can be converted to like fractions using the LCM method.
Practice Problems
- Identify the like fractions: 2/7, 3/5, 5/7, 1/7, 4/9.
- Are 5/6 and 7/6 like or unlike fractions?
- Convert 1/4 and 2/5 to like fractions.
- Which is greater: 3/7 or 4/7?
- Convert 2/3, 3/5, and 1/2 to like fractions.
- Arrange in ascending order: 5/12, 1/12, 11/12, 7/12.
Frequently Asked Questions
Q1. What are like fractions?
Like fractions are fractions with the same denominator. For example, 2/5, 3/5, and 4/5 are like fractions because they all have 5 as the denominator.
Q2. What are unlike fractions?
Unlike fractions are fractions with different denominators. For example, 1/3, 2/5, and 3/7 are unlike fractions.
Q3. How do you compare unlike fractions?
Convert them to like fractions by finding the LCM of their denominators. Then compare the numerators. The fraction with the larger numerator is greater.
Q4. Can like fractions have different numerators?
Yes. Like fractions must have the same denominator, but the numerators can be different. For example, 1/8, 3/8, and 5/8 are all like fractions with different numerators.
Q5. Why do we need to convert unlike fractions to like fractions?
You cannot add, subtract, or easily compare fractions with different denominators. Converting to like fractions (same denominator) makes these operations possible.
Q6. What is the LCM method?
LCM stands for Least Common Multiple. Find the LCM of the denominators, then multiply the numerator and denominator of each fraction to get the LCM as the new denominator. This gives equivalent like fractions.
