Adding Like Fractions (Grade 3)
Like fractions are fractions that have the same denominator (same bottom number). Adding like fractions is the first type of fraction addition that students learn in Class 3.
When fractions have the same denominator, adding them is simple — just add the numerators (top numbers) and keep the denominator the same.
Think of it like this: if you have 2 slices of a pizza cut into 8 pieces, and someone gives you 3 more slices of the same pizza, you now have 5 slices out of 8. That is 2/8 + 3/8 = 5/8.
What is Adding Like Fractions - Class 3 Maths (Fractions (Grade 3))?
Like fractions have the same denominator. To add them:
a/d + b/d = (a + b)/d
Add the numerators. Keep the denominator the same.
Example: 1/5 + 2/5 = (1 + 2)/5 = 3/5
The denominator stays as 5 because the size of each part has not changed — only the number of parts has increased.
Types and Properties
Types of Like Fraction Addition
1. Simple Addition (answer less than 1)
The sum is a proper fraction (numerator smaller than denominator).
- 1/6 + 2/6 = 3/6
- 2/8 + 3/8 = 5/8
2. Adding to Get a Whole
When the numerators add up to equal the denominator, the sum is 1.
- 3/4 + 1/4 = 4/4 = 1
- 5/5 = 1
3. Adding More Than Two Fractions
The same rule works for three or more like fractions.
- 1/6 + 2/6 + 1/6 = (1 + 2 + 1)/6 = 4/6
Solved Examples
Example 1: Example 1: Basic Addition
Question: Find 1/5 + 3/5.
Think:
- Same denominator (5) → add numerators
- 1 + 3 = 4
- Answer = 4/5
Answer: 1/5 + 3/5 = 4/5
Example 2: Example 2: Adding to Get a Whole
Question: Find 2/3 + 1/3.
Think:
- Same denominator (3)
- 2 + 1 = 3
- 3/3 = 1 whole
Answer: 2/3 + 1/3 = 3/3 = 1
Example 3: Example 3: Larger Denominator
Question: Find 3/10 + 4/10.
Think:
- Same denominator (10)
- 3 + 4 = 7
- Answer = 7/10
Answer: 3/10 + 4/10 = 7/10
Example 4: Example 4: Word Problem – Cake Slices
Question: Ria eats 2/8 of a cake. Meera eats 3/8 of the same cake. What fraction of the cake did they eat together?
Think:
- Both fractions have denominator 8
- 2/8 + 3/8 = (2 + 3)/8 = 5/8
Answer: They ate 5/8 of the cake together.
Example 5: Example 5: Adding Three Fractions
Question: Find 1/6 + 2/6 + 2/6.
Think:
- All have denominator 6
- 1 + 2 + 2 = 5
- Answer = 5/6
Answer: 1/6 + 2/6 + 2/6 = 5/6
Example 6: Example 6: Word Problem – Ribbon
Question: Aditi uses 2/7 of a ribbon for a bow and 4/7 for a gift. What fraction of the ribbon did she use?
Think:
- Same denominator (7)
- 2/7 + 4/7 = 6/7
Answer: Aditi used 6/7 of the ribbon.
Example 7: Example 7: Visual Understanding
Question: A circle is divided into 5 equal parts. 1 part is coloured red and 2 parts are coloured blue. What fraction is coloured in total?
Think:
- Red = 1/5, Blue = 2/5
- Total coloured = 1/5 + 2/5 = 3/5
Answer: 3/5 of the circle is coloured.
Example 8: Example 8: Zero Numerator
Question: Find 0/4 + 3/4.
Think:
- 0 + 3 = 3
- Answer = 3/4
Answer: 0/4 + 3/4 = 3/4
Example 9: Example 9: Word Problem – Water Bottle
Question: Rahul drinks 3/10 of a water bottle in the morning and 4/10 in the afternoon. What fraction has he drunk?
Think:
- 3/10 + 4/10 = 7/10
Answer: Rahul has drunk 7/10 of the bottle.
Example 10: Example 10: Finding the Missing Numerator
Question: 2/9 + ?/9 = 5/9. Find the missing fraction.
Think:
- 2 + ? = 5
- ? = 5 − 2 = 3
- Missing fraction = 3/9
Answer: The missing fraction is 3/9.
Real-World Applications
Where Do We Add Like Fractions?
- Sharing food: Combining fractions of a pizza or cake that different people ate.
- Measuring: Adding lengths when both are given as fractions with the same denominator.
- Colouring: Finding total coloured area when parts of a shape are coloured differently.
- Time: Adding parts of an hour (e.g., 1/4 hour + 2/4 hour = 3/4 hour).
Key Points to Remember
- Like fractions have the same denominator.
- To add like fractions: add the numerators, keep the denominator.
- If the numerator equals the denominator, the fraction equals 1 whole.
- Adding 0 to any fraction gives the same fraction: 0/d + a/d = a/d.
- You can add more than two like fractions the same way.
- Always check: are the denominators the same? If yes, just add the top numbers.
Practice Problems
- Find 2/7 + 3/7.
- Find 4/9 + 5/9.
- Find 1/6 + 3/6 + 1/6.
- Priya reads 3/8 of a book on Monday and 2/8 on Tuesday. What fraction has she read?
- Find 5/12 + 4/12.
- Dev eats 1/4 of a cake and Kavi eats 2/4. What fraction is eaten?
- Find the missing number: 3/10 + ?/10 = 8/10.
- Neha paints 2/5 of a wall in the morning and 2/5 in the evening. What fraction is painted?
Frequently Asked Questions
Q1. What are like fractions?
Like fractions are fractions that have the same denominator (bottom number). For example, 2/7 and 5/7 are like fractions because both have 7 as the denominator.
Q2. How do you add like fractions?
Add the numerators (top numbers) and keep the denominator the same. For example, 3/8 + 2/8 = 5/8.
Q3. Why does the denominator stay the same?
The denominator tells you the size of each part. When adding, the size of the parts does not change — only the number of parts increases. So the denominator stays the same.
Q4. What happens when the sum equals the denominator?
When the numerator equals the denominator, the fraction equals 1 whole. For example, 3/5 + 2/5 = 5/5 = 1.
Q5. Can the answer be more than 1?
In Class 3, most problems give answers less than or equal to 1. But yes, 5/4 + 2/4 = 7/4, which is more than 1. This is called an improper fraction.
Q6. Can I add fractions with different denominators?
Not directly using this method. You must first make the denominators the same (find a common denominator). This is taught in higher classes.
Q7. Is 2/6 + 3/6 the same as 5/6?
Yes. Add the numerators: 2 + 3 = 5. Keep the denominator: 6. So 2/6 + 3/6 = 5/6.
Q8. How do I check my answer?
Make sure the denominator in your answer matches the original denominator. Also check that the numerator equals the sum of the original numerators.
Q9. Can I add three or more like fractions?
Yes. Just add all the numerators and keep the denominator the same. For example, 1/8 + 3/8 + 2/8 = 6/8.
