Comparing Fractions (Grade 3)
Comparing fractions means finding out which fraction is bigger, smaller, or if they are equal. In Class 3, you learn to compare fractions that have the same denominator (like fractions) and fractions that have the same numerator.
You use the symbols > (greater than), < (less than), and = (equal to) to show the comparison.
What is Comparing Fractions - Class 3 Maths (Fractions)?
Comparing fractions is deciding which fraction represents a bigger or smaller part of the whole.
Rule 1 — Same denominator: The fraction with the larger numerator is greater.
Same denominator: bigger numerator = bigger fraction
Rule 2 — Same numerator: The fraction with the smaller denominator is greater.
Same numerator: smaller denominator = bigger fraction
Solved Examples
Example 1: Same Denominator — Compare
Question: Which is greater: 3/7 or 5/7?
Think:
- Both fractions have denominator 7 (same-sized parts).
- 5 parts > 3 parts
Answer: 5/7 > 3/7.
Example 2: Same Denominator — Ordering
Question: Arrange in order from smallest to largest: 4/9, 2/9, 7/9, 1/9.
Think:
- All have denominator 9. Compare numerators: 1, 2, 4, 7.
Answer: 1/9 < 2/9 < 4/9 < 7/9.
Example 3: Same Numerator — Compare
Question: Which is greater: 1/3 or 1/5?
Think:
- Both have numerator 1. The one with the smaller denominator gives bigger pieces.
- 1/3 has bigger pieces than 1/5.
Answer: 1/3 > 1/5.
Example 4: Same Numerator — Ordering
Question: Arrange from largest to smallest: 2/3, 2/7, 2/5, 2/4.
Think:
- All have numerator 2. Smaller denominator = larger fraction.
- Order of denominators: 3 < 4 < 5 < 7.
Answer: 2/3 > 2/4 > 2/5 > 2/7.
Example 5: Using Pictures
Question: Two identical rectangles are divided into 4 equal parts each. Rectangle A has 1 part shaded. Rectangle B has 3 parts shaded. Which shows a larger fraction?
Think:
- A = 1/4, B = 3/4
- 3/4 > 1/4
Answer: Rectangle B (3/4) shows the larger fraction.
Example 6: Word Problem
Question: Ria ate 2/6 of a cake. Priya ate 4/6 of the same cake. Who ate more?
Think:
- Same denominator (6). Compare numerators: 4 > 2.
Answer: Priya ate more (4/6 > 2/6).
Example 7: Comparing with 1/2
Question: Is 3/8 greater than or less than 1/2?
Think:
- 1/2 = 4/8 (make the denominators the same)
- 3/8 < 4/8
Answer: 3/8 < 1/2.
Example 8: Equal Fractions
Question: Compare 3/5 and 3/5.
Think:
- Same numerator and same denominator.
- They are equal.
Answer: 3/5 = 3/5.
Example 9: Word Problem — Tiffin
Question: Aman's tiffin box is 3/4 full. Dev's tiffin box is 1/4 full. Whose box has more food?
Think:
- Same denominator (4). Numerators: 3 > 1.
Answer: Aman's box has more food (3/4 > 1/4).
Key Points to Remember
- When denominators are the same, compare numerators — larger numerator = larger fraction.
- When numerators are the same, compare denominators — smaller denominator = larger fraction.
- Use >, <, or = to write comparisons.
- Drawing pictures (shaded shapes) helps visualise which fraction is bigger.
- 1/2 is a useful benchmark for quick comparisons.
- Equal fractions have the same numerator AND denominator (or are equivalent).
Practice Problems
- Which is greater: 5/8 or 3/8?
- Which is greater: 1/4 or 1/6?
- Arrange from smallest to largest: 3/10, 7/10, 1/10, 5/10.
- Compare 2/5 and 2/9. Which is larger?
- Priya reads 5/9 of a book. Meera reads 7/9. Who reads more?
- Is 3/6 greater than, less than, or equal to 1/2?
- Arrange from largest to smallest: 3/4, 3/8, 3/5, 3/6.
Frequently Asked Questions
Q1. How do I compare fractions with the same denominator?
Look at the numerators. The fraction with the bigger numerator is the bigger fraction. For example, 5/9 > 3/9 because 5 > 3.
Q2. How do I compare fractions with the same numerator?
Look at the denominators. The fraction with the smaller denominator is bigger. For example, 2/3 > 2/5 because thirds are bigger pieces than fifths.
Q3. Why does a smaller denominator give a bigger fraction?
Because dividing something into fewer parts makes each part larger. Half a roti is bigger than a quarter of the same roti.
Q4. How do I compare fractions with different numerators AND different denominators?
In Class 3, you mainly compare fractions with the same denominator or same numerator. For others, you can make the denominators the same (which you learn more about in Class 4).
Q5. What does the symbol > mean?
It means 'greater than'. The wide open side faces the bigger number. 5/7 > 3/7 means 5/7 is greater than 3/7.
Q6. Can I use pictures to compare fractions?
Yes. Draw two identical shapes, divide them into the same number of parts, shade the fractions, and see which has more area shaded.
Q7. What is a benchmark fraction?
A benchmark is a commonly used fraction like 1/2 or 1/4 that helps you estimate. If a fraction is more than 1/2, it is more than half.
Q8. Is comparing fractions covered in NCERT Class 3?
Yes. NCERT Class 3 Maths teaches comparing like fractions (same denominator) and introduces the idea using pictures and number lines.
