Comparing Fractions (Grade 4)
Comparing fractions means finding out which fraction is greater, smaller, or if they are equal. In Class 4, you will learn to compare like fractions (same denominator), unlike fractions (different denominators), and unit fractions.
The symbols used are: > (greater than), < (less than), and = (equal to).
What is Comparing Fractions - Class 4 Maths (Fractions)?
To compare fractions means to determine which fraction represents a larger or smaller part of a whole.
Rules:
- Like fractions (same denominator): Compare the numerators. The fraction with the larger numerator is greater.
- Unit fractions (same numerator = 1): The fraction with the smaller denominator is greater.
- Unlike fractions (different denominators): Convert to like fractions (find LCM of denominators) or use cross multiplication.
Comparing Fractions (Grade 4) Formula
Cross Multiplication: Compare a/b and c/d → Compare a × d with b × c
Solved Examples
Example 1: Example 1: Comparing Like Fractions
Problem: Compare 3/7 and 5/7.
Solution:
Step 1: Both fractions have denominator 7 (like fractions).
Step 2: Compare numerators: 3 and 5. Since 5 > 3.
Answer: 3/7 < 5/7
Example 2: Example 2: Comparing Unit Fractions
Problem: Compare 1/4 and 1/6.
Solution:
Step 1: Both are unit fractions (numerator = 1).
Step 2: For unit fractions, smaller denominator = larger fraction.
Step 3: 4 < 6, so 1/4 > 1/6.
Answer: 1/4 > 1/6
Example 3: Example 3: Unlike Fractions Using LCM
Problem: Compare 2/3 and 3/4.
Solution:
Step 1: LCM of 3 and 4 = 12.
Step 2: Convert: 2/3 = (2×4)/(3×4) = 8/12.
Step 3: Convert: 3/4 = (3×3)/(4×3) = 9/12.
Step 4: Compare: 8/12 and 9/12. Since 8 < 9.
Answer: 2/3 < 3/4
Example 4: Example 4: Cross Multiplication
Problem: Compare 5/8 and 3/5 using cross multiplication.
Solution:
Step 1: Cross multiply: 5 × 5 = 25 and 8 × 3 = 24.
Step 2: 25 > 24.
Answer: 5/8 > 3/5
Example 5: Example 5: Fractions Equal to Each Other
Problem: Compare 4/6 and 2/3.
Solution:
Step 1: Simplify 4/6: HCF = 2. 4÷2 / 6÷2 = 2/3.
Step 2: Both fractions are 2/3.
Answer: 4/6 = 2/3
Example 6: Example 6: Same Numerator, Different Denominators
Problem: Compare 3/5 and 3/8.
Solution:
Step 1: Both have numerator 3.
Step 2: When numerators are equal, the fraction with the smaller denominator is greater.
Step 3: 5 < 8, so 3/5 > 3/8.
Answer: 3/5 > 3/8
Example 7: Example 7: Word Problem
Problem: Aman ate 2/5 of a cake and Ria ate 3/7 of the same cake. Who ate more?
Solution:
Step 1: Compare 2/5 and 3/7 using cross multiplication.
Step 2: 2 × 7 = 14 and 5 × 3 = 15.
Step 3: 14 < 15.
Answer: 2/5 < 3/7, so Ria ate more.
Example 8: Example 8: Word Problem
Problem: Kavi completed 5/6 of his homework and Neha completed 7/8 of hers. Who completed a greater fraction?
Solution:
Step 1: LCM of 6 and 8 = 24.
Step 2: 5/6 = 20/24 and 7/8 = 21/24.
Step 3: 20/24 < 21/24.
Answer: Neha completed a greater fraction (7/8 > 5/6).
Example 9: Example 9: Comparing a Fraction with 1/2
Problem: Is 5/9 greater than or less than 1/2?
Solution:
Step 1: Cross multiply: 5 × 2 = 10 and 9 × 1 = 9.
Step 2: 10 > 9.
Answer: 5/9 > 1/2
Key Points to Remember
- For like fractions, compare numerators — larger numerator means larger fraction.
- For unit fractions, smaller denominator means larger fraction.
- For unlike fractions, convert to like fractions using LCM or use cross multiplication.
- When numerators are the same, the fraction with the smaller denominator is greater.
- Cross multiplication is a quick method: for a/b and c/d, compare a×d with b×c.
- Always simplify fractions first to check if they might be equal.
Practice Problems
- Compare 4/9 and 7/9.
- Compare 1/5 and 1/8. Which is greater?
- Compare 3/4 and 5/7 using cross multiplication.
- Compare 2/6 and 1/3. What do you notice?
- Priya drank 3/8 of a glass of milk and Dev drank 2/5. Who drank more?
- Arrange in ascending order: 1/2, 2/5, 3/4.
- Is 7/12 greater than or less than 1/2?
Frequently Asked Questions
Q1. How do you compare fractions with the same denominator?
When denominators are the same, simply compare the numerators. The fraction with the larger numerator is the greater fraction. For example, 5/8 > 3/8 because 5 > 3.
Q2. How do you compare fractions with different denominators?
Either find the LCM of the denominators and convert both fractions to like fractions, or use cross multiplication. Then compare the resulting numerators.
Q3. What is cross multiplication for comparing fractions?
To compare a/b and c/d, calculate a x d and b x c. If a x d > b x c, then a/b > c/d. If they are equal, the fractions are equal.
Q4. Which is larger: 1/3 or 1/5?
1/3 is larger. With unit fractions (numerator = 1), the fraction with the smaller denominator represents a bigger piece, so 1/3 > 1/5.
Q5. How do you compare a fraction with 1/2?
A fraction a/b is greater than 1/2 if 2a > b. It equals 1/2 if 2a = b. It is less than 1/2 if 2a < b. Example: 5/8, check 2 x 5 = 10 > 8, so 5/8 > 1/2.
Q6. Can you compare fractions on a number line?
Yes. Plot both fractions on the same number line. The fraction that is farther to the right is the greater one.
Q7. What if two fractions are equivalent?
If two fractions simplify to the same fraction, they are equal. For example, 4/6 and 2/3 are equal because 4/6 simplifies to 2/3.
Q8. When do we need to compare fractions in real life?
When deciding which pizza slice is bigger, comparing test scores (like 7/10 vs 13/20), or checking which jug has more juice (3/4 litre vs 2/3 litre).
Q9. Is comparing fractions in the NCERT Class 4 syllabus?
Yes. Comparing fractions is an important part of the Class 4 Fractions chapter. Students learn to compare like fractions, unlike fractions, and unit fractions.
Related Topics
- Simplifying Fractions
- Ordering Fractions
- Fractions (Grade 4)
- Equivalent Fractions (Grade 4)
- Addition of Fractions (Grade 4)
- Subtraction of Fractions (Grade 4)
- Mixed Numbers and Improper Fractions
- Fraction Word Problems (Grade 4)
- Fractions on a Number Line (Grade 4)
- Proper and Improper Fractions
- Fraction of a Number (Grade 4)
