Adding Unlike Fractions

Class 5Fractions (Grade 5)

Adding unlike fractions means adding two or more fractions that have different denominators. Unlike fractions cannot be added directly — you must first convert them to like fractions (same denominator) by finding the LCM of the denominators.

This is one of the most important fraction skills in Class 5 and forms the basis for more complex operations like adding mixed numbers and working with decimals.

Think of it this way: if you have 1/3 of a pizza and 1/4 of the same pizza, you cannot simply say you have 2/7 of a pizza. The slices are different sizes! To add them, you need to cut both portions into equal-sized pieces first. That is exactly what finding a common denominator does — it makes the pieces the same size so they can be counted together.

In Class 4, students mastered adding like fractions (same denominator). Now in Class 5, the denominators are different, so an extra step — finding the LCM — is needed before adding.

What is Adding Unlike Fractions - Class 5 Maths (Fractions)?

Unlike fractions are fractions with different denominators (e.g., 2/3 and 3/5).

To add unlike fractions, follow these steps:

Find the LCM of the denominators.
Convert each fraction to an equivalent fraction with the LCM as the denominator.
Add the numerators. Keep the denominator the same.
Simplify the result if possible.

a/b + c/d = (a×d + c×b) / (b×d)
Or use LCM method for simpler denominators

Adding Unlike Fractions Formula

Step-by-Step Method:
1. Find LCM of denominators
2. Convert to equivalent fractions with LCM as denominator
3. Add numerators
4. Simplify if needed

Types and Properties

Case 1: One denominator is a multiple of the other

Example: 1/3 + 5/6. Since 6 is a multiple of 3, convert 1/3 to 2/6 and add: 2/6 + 5/6 = 7/6.

Case 2: Denominators are co-prime

Example: 2/3 + 1/5. LCM of 3 and 5 = 15. Convert: 10/15 + 3/15 = 13/15.

Case 3: Denominators share a common factor (not multiples of each other)

Example: 3/4 + 5/6. LCM of 4 and 6 = 12. Convert: 9/12 + 10/12 = 19/12 = 1 7/12.

Case 4: Adding more than two fractions

Find the LCM of all denominators, convert all fractions, then add all numerators.

Solved Examples

Example 1: Example 1: Simple Unlike Fractions

Problem: Calculate 1/4 + 2/3.

Solution:

Step 1: LCM of 4 and 3 = 12.

Step 2: Convert: 1/4 = 3/12 and 2/3 = 8/12.

Step 3: Add: 3/12 + 8/12 = 11/12.

Answer: 1/4 + 2/3 = 11/12

Example 2: Example 2: One Denominator Is a Multiple

Problem: Calculate 3/5 + 7/10.

Solution:

Step 1: LCM of 5 and 10 = 10 (since 10 is a multiple of 5).

Step 2: Convert: 3/5 = 6/10. The other fraction is already 7/10.

Step 3: Add: 6/10 + 7/10 = 13/10 = 1 3/10.

Answer: 3/5 + 7/10 = 1 3/10

Example 3: Example 3: Result Needs Simplification

Problem: Calculate 1/6 + 3/8.

Solution:

Step 1: LCM of 6 and 8 = 24.

Step 2: Convert: 1/6 = 4/24 and 3/8 = 9/24.

Step 3: Add: 4/24 + 9/24 = 13/24.

Step 4: Check: HCF(13, 24) = 1. Already in simplest form.

Answer: 1/6 + 3/8 = 13/24

Example 4: Example 4: Sum Greater Than 1

Problem: Calculate 5/6 + 3/4.

Solution:

Step 1: LCM of 6 and 4 = 12.

Step 2: Convert: 5/6 = 10/12 and 3/4 = 9/12.

Step 3: Add: 10/12 + 9/12 = 19/12.

Step 4: Convert to mixed number: 19/12 = 1 7/12.

Answer: 5/6 + 3/4 = 1 7/12

Example 5: Example 5: Adding Three Unlike Fractions

Problem: Calculate 1/2 + 1/3 + 1/4.

Solution:

Step 1: LCM of 2, 3, and 4 = 12.

Step 2: Convert:

1/2 = 6/12
1/3 = 4/12
1/4 = 3/12

Step 3: Add: 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12.

Answer: 1/2 + 1/3 + 1/4 = 1 1/12

Example 6: Example 6: Word Problem — Sharing a Cake

Problem: Aditi ate 1/3 of a cake and Priya ate 1/4 of the same cake. What fraction did they eat together?

Solution:

Step 1: Total eaten = 1/3 + 1/4.

Step 2: LCM of 3 and 4 = 12.

Step 3: Convert: 1/3 = 4/12 and 1/4 = 3/12.

Step 4: Add: 4/12 + 3/12 = 7/12.

Answer: Together they ate 7/12 of the cake.

Example 7: Example 7: Word Problem — Distance

Problem: Rahul walked 2/5 km in the morning and 1/3 km in the evening. What is the total distance he walked?

Solution:

Step 1: Total = 2/5 + 1/3.

Step 2: LCM of 5 and 3 = 15.

Step 3: Convert: 2/5 = 6/15 and 1/3 = 5/15.

Step 4: Add: 6/15 + 5/15 = 11/15.

Answer: Rahul walked 11/15 km in total.

Example 8: Example 8: With Simplification

Problem: Calculate 5/8 + 1/4.

Solution:

Step 1: LCM of 8 and 4 = 8.

Step 2: Convert: 1/4 = 2/8. The other fraction is already 5/8.

Step 3: Add: 5/8 + 2/8 = 7/8.

Answer: 5/8 + 1/4 = 7/8

Example 9: Example 9: Whole Number + Fraction

Problem: Calculate 2 + 3/7.

Solution:

Step 1: Write 2 as a fraction: 2 = 14/7.

Step 2: Add: 14/7 + 3/7 = 17/7.

Step 3: Convert to mixed number: 17/7 = 2 3/7.

Answer: 2 + 3/7 = 2 3/7

Example 10: Example 10: Word Problem — Money

Problem: Meera spent 1/3 of her pocket money on a notebook and 2/5 on a pen. What fraction of her pocket money did she spend?

Solution:

Step 1: Total spent = 1/3 + 2/5.

Step 2: LCM of 3 and 5 = 15.

Step 3: Convert: 1/3 = 5/15 and 2/5 = 6/15.

Step 4: Add: 5/15 + 6/15 = 11/15.

Answer: Meera spent 11/15 of her pocket money.

Real-World Applications

Where adding unlike fractions is used:

Cooking: Combining different measurements — 1/3 cup water + 1/4 cup milk
Distance: Adding distances walked in different intervals
Money: Combining fractional portions of spending
Time: Adding time periods expressed as fractions of an hour
Science: Combining measurements from different experiments

Key Points to Remember

Unlike fractions have different denominators — they cannot be added directly.
Step 1: Find the LCM of the denominators.
Step 2: Convert each fraction to an equivalent fraction with the LCM as denominator.
Step 3: Add the numerators. Keep the common denominator.
Step 4: Simplify the result if possible.
If the sum is an improper fraction, convert it to a mixed number.
Never add numerators and denominators separately (1/3 + 1/4 is NOT 2/7).
If one denominator is a multiple of the other, the LCM is just the larger denominator.

Practice Problems

Calculate 2/5 + 1/3.
Add 3/8 + 5/12.
Find the sum: 1/6 + 2/9.
Kavi drank 1/4 litre of juice and 2/5 litre of water. How much liquid did he drink in total?
Calculate 3/7 + 2/3 + 1/21.
Ria completed 2/5 of her homework before dinner and 3/10 after dinner. What fraction has she completed?
Add 5/6 + 7/8 and express as a mixed number.
Arjun spent 1/4 of his day at school and 1/6 of his day playing cricket. What fraction of the day was this?

Frequently Asked Questions

Q1. What are unlike fractions?

Unlike fractions are fractions that have different denominators. For example, 2/3 and 4/5 are unlike fractions because their denominators (3 and 5) are different.

Q2. Why can't we add unlike fractions directly?

Because the denominators represent different-sized parts. 1/3 and 1/4 represent different sizes, so you cannot add them until they represent the same-sized parts. Converting to a common denominator makes the parts equal.

Q3. What is the most common mistake when adding unlike fractions?

The most common mistake is adding both numerators and denominators: writing 1/3 + 1/4 = 2/7. This is wrong. You must first find a common denominator, then add only the numerators.

Q4. Why do we use LCM and not just multiply the denominators?

Multiplying the denominators always gives a common denominator, but it may not be the smallest one. Using LCM gives the Least Common Denominator (LCD), which keeps numbers smaller and easier to work with.

Q5. What if the answer is an improper fraction?

Convert it to a mixed number. For example, if you get 11/4, divide: 11 ÷ 4 = 2 remainder 3, so the answer is 2 3/4.

Q6. How do I add a whole number and a fraction?

Write the whole number as a fraction with the same denominator. For example, 3 + 2/5: write 3 as 15/5, then add: 15/5 + 2/5 = 17/5 = 3 2/5.

Q7. Can I add three or more unlike fractions?

Yes. Find the LCM of all the denominators, convert each fraction, then add all the numerators. For example, for 1/2 + 1/3 + 1/5, LCM = 30, giving 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30.

Q8. Should I always simplify the final answer?

Yes. Always check if the numerator and denominator have a common factor. If they do, divide both by the HCF to get the simplest form.

Q9. Is this topic covered in the NCERT Class 5 textbook?

Yes. Adding unlike fractions is a core topic in the Fractions chapter of NCERT Class 5 Mathematics, building on the concepts of equivalent fractions and LCM.

Adding Unlike Fractions

What is Adding Unlike Fractions - Class 5 Maths (Fractions)?

Adding Unlike Fractions Formula

Types and Properties

Solved Examples

Example 1: Example 1: Simple Unlike Fractions

Example 2: Example 2: One Denominator Is a Multiple

Example 3: Example 3: Result Needs Simplification

Example 4: Example 4: Sum Greater Than 1

Example 5: Example 5: Adding Three Unlike Fractions

Example 6: Example 6: Word Problem — Sharing a Cake

Example 7: Example 7: Word Problem — Distance

Example 8: Example 8: With Simplification

Example 9: Example 9: Whole Number + Fraction

Example 10: Example 10: Word Problem — Money

Real-World Applications

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. What are unlike fractions?

Q2. Why can't we add unlike fractions directly?

Q3. What is the most common mistake when adding unlike fractions?

Q4. Why do we use LCM and not just multiply the denominators?

Q5. What if the answer is an improper fraction?

Q6. How do I add a whole number and a fraction?

Q7. Can I add three or more unlike fractions?

Q8. Should I always simplify the final answer?

Q9. Is this topic covered in the NCERT Class 5 textbook?

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