Subtracting Unlike Fractions
Subtracting unlike fractions means finding the difference between two fractions that have different denominators. Just like addition, you cannot subtract unlike fractions directly — you must first convert them to like fractions using the LCM of the denominators.
This skill is essential in Class 5 and is used in word problems involving remaining quantities, differences in measurements, and fraction comparisons.
In earlier classes, students learned to subtract like fractions (same denominator) by simply subtracting the numerators. Now in Class 5, the challenge increases because the denominators are different. The key idea is: convert unlike fractions to like fractions first, then subtract as usual.
Consider this: if Ria has 3/4 of a chocolate bar and eats 1/3, how much is left? Since 3/4 and 1/3 have different denominators, you cannot simply write 3/4 − 1/3 = 2/1. That would be wrong! Instead, you must find a common denominator, convert both fractions, and then subtract.
What is Subtracting Unlike Fractions - Class 5 Maths (Fractions)?
Unlike fractions are fractions that have different denominators, such as 2/5 and 3/7, or 1/4 and 5/6. The denominators tell us the size of each part — fifths are different from sevenths. Since the parts are of different sizes, we cannot subtract them directly.
To subtract unlike fractions, follow these steps:
- Find the LCM (Lowest Common Multiple) of the denominators. This becomes the common denominator.
- Convert each fraction to an equivalent fraction with the LCM as its denominator. Multiply both numerator and denominator by the same factor.
- Subtract the numerators. The denominator stays the same.
- Simplify the result to its lowest terms. Check if the numerator and denominator have a common factor.
a/b − c/d = (a×d − c×b) / (b×d)
Or use LCM method for simpler numbers
Why LCM and not just the product? Using the LCM gives the smallest common denominator, which keeps the numbers manageable. For example, for 5/6 − 1/4, the product 6 × 4 = 24 works, but the LCM is 12 — much easier to calculate with.
Subtracting Unlike Fractions Formula
Step-by-Step Method:
1. Find LCM of denominators
2. Convert to equivalent fractions
3. Subtract numerators
4. Simplify if needed
Types and Properties
Case 1: One denominator is a multiple of the other
Example: 5/6 − 1/3. Since 6 is a multiple of 3, convert 1/3 to 2/6. Result: 5/6 − 2/6 = 3/6 = 1/2.
Case 2: Denominators are co-prime
Example: 3/4 − 2/7. LCM of 4 and 7 = 28. Convert: 21/28 − 8/28 = 13/28.
Case 3: Denominators share a common factor
Example: 7/8 − 2/6. LCM of 8 and 6 = 24. Convert: 21/24 − 8/24 = 13/24.
Case 4: Subtracting from a whole number
Example: 1 − 3/5 = 5/5 − 3/5 = 2/5.
Solved Examples
Example 1: Example 1: Simple Unlike Fractions
Problem: Calculate 3/4 − 1/3.
Solution:
Step 1: LCM of 4 and 3 = 12.
Step 2: Convert: 3/4 = 9/12 and 1/3 = 4/12.
Step 3: Subtract: 9/12 − 4/12 = 5/12.
Answer: 3/4 − 1/3 = 5/12
Example 2: Example 2: One Denominator Is a Multiple
Problem: Calculate 7/10 − 2/5.
Solution:
Step 1: LCM of 10 and 5 = 10.
Step 2: Convert: 2/5 = 4/10. The other fraction is already 7/10.
Step 3: Subtract: 7/10 − 4/10 = 3/10.
Answer: 7/10 − 2/5 = 3/10
Example 3: Example 3: Result Needs Simplification
Problem: Calculate 5/6 − 1/4.
Solution:
Step 1: LCM of 6 and 4 = 12.
Step 2: Convert: 5/6 = 10/12 and 1/4 = 3/12.
Step 3: Subtract: 10/12 − 3/12 = 7/12.
Step 4: HCF(7, 12) = 1. Already in simplest form.
Answer: 5/6 − 1/4 = 7/12
Example 4: Example 4: Subtracting from 1
Problem: A jug was full. Priya poured out 3/8 of the water. What fraction remains?
Solution:
Step 1: Remaining = 1 − 3/8.
Step 2: Write 1 as 8/8.
Step 3: Subtract: 8/8 − 3/8 = 5/8.
Answer: 5/8 of the water remains.
Example 5: Example 5: With Simplification
Problem: Calculate 7/8 − 3/4.
Solution:
Step 1: LCM of 8 and 4 = 8.
Step 2: Convert: 3/4 = 6/8.
Step 3: Subtract: 7/8 − 6/8 = 1/8.
Answer: 7/8 − 3/4 = 1/8
Example 6: Example 6: Word Problem — Distance
Problem: Dev walked 4/5 km. Aman walked 1/3 km. How much more did Dev walk?
Solution:
Step 1: Difference = 4/5 − 1/3.
Step 2: LCM of 5 and 3 = 15.
Step 3: Convert: 4/5 = 12/15 and 1/3 = 5/15.
Step 4: Subtract: 12/15 − 5/15 = 7/15.
Answer: Dev walked 7/15 km more than Aman.
Example 7: Example 7: Word Problem — Sharing
Problem: Neha had 5/6 of a chocolate bar. She gave 1/4 of the whole bar to her brother. How much does she have now?
Solution:
Step 1: Remaining = 5/6 − 1/4.
Step 2: LCM of 6 and 4 = 12.
Step 3: Convert: 5/6 = 10/12 and 1/4 = 3/12.
Step 4: Subtract: 10/12 − 3/12 = 7/12.
Answer: Neha has 7/12 of the chocolate bar left.
Example 8: Example 8: Co-prime Denominators
Problem: Calculate 5/7 − 2/9.
Solution:
Step 1: 7 and 9 are co-prime, so LCM = 7 × 9 = 63.
Step 2: Convert: 5/7 = 45/63 and 2/9 = 14/63.
Step 3: Subtract: 45/63 − 14/63 = 31/63.
Answer: 5/7 − 2/9 = 31/63
Example 9: Example 9: Word Problem — Fraction Remaining
Problem: Ria used 2/3 of a sheet of coloured paper for a craft project and 1/6 for decorating a card. What fraction of the paper is left?
Solution:
Step 1: Total used = 2/3 + 1/6. LCM of 3 and 6 = 6.
Step 2: 2/3 = 4/6. So total used = 4/6 + 1/6 = 5/6.
Step 3: Paper left = 1 − 5/6 = 6/6 − 5/6 = 1/6.
Answer: 1/6 of the paper is left.
Example 10: Example 10: Larger Denominators
Problem: Calculate 11/12 − 3/8.
Solution:
Step 1: LCM of 12 and 8 = 24.
Step 2: Convert: 11/12 = 22/24 and 3/8 = 9/24.
Step 3: Subtract: 22/24 − 9/24 = 13/24.
Answer: 11/12 − 3/8 = 13/24
Real-World Applications
Where subtracting unlike fractions is used:
- Finding remainders: How much is left after using a fraction of something
- Comparing: How much more one person has compared to another
- Cooking: Adjusting recipes — "I need 3/4 cup but only have 1/3 cup"
- Distance: Finding how much further one person walked or ran
- Time: Calculating remaining time from a fractional hour
Key Points to Remember
- Unlike fractions have different denominators — convert to like fractions before subtracting.
- Find the LCM of the denominators to get the common denominator.
- Convert each fraction to an equivalent fraction with the common denominator.
- Subtract the numerators only. The denominator stays the same.
- Always simplify the result if possible.
- To subtract a fraction from 1: write 1 as a fraction with the same denominator (e.g., 1 = 8/8).
- The larger fraction must come first — you cannot subtract a larger fraction from a smaller one (at this level).
- Check your answer: the result must be less than the first fraction.
Practice Problems
- Calculate 4/5 − 2/3.
- Subtract 3/8 from 5/6.
- Find: 7/9 − 1/6.
- Aditi had 3/4 of a pizza. She ate 1/3 of the whole pizza. What fraction is left?
- A tank is 5/6 full. After Rahul uses some water, it is 1/2 full. What fraction of water did he use?
- Calculate 11/12 − 5/8.
- Kavi studied for 2/3 of an hour. Dev studied for 5/12 of an hour. How much longer did Kavi study?
- Subtract: 1 − 4/7.
Frequently Asked Questions
Q1. How is subtracting unlike fractions different from subtracting like fractions?
Like fractions already have the same denominator, so you subtract numerators directly. Unlike fractions need to be converted to like fractions first using the LCM of the denominators.
Q2. What if I get a negative answer?
At the Class 5 level, always subtract the smaller fraction from the larger one. If you get a negative answer, check whether you placed the fractions in the correct order.
Q3. Do I need to simplify the answer?
Yes. Always check if the numerator and denominator share a common factor. If they do, divide both by the HCF to get the simplest form.
Q4. Can I use cross multiplication for subtraction?
Yes. For a/b − c/d, the answer is (a×d − c×b) / (b×d). However, using LCM often gives smaller numbers that are easier to work with.
Q5. How do I subtract a fraction from a whole number?
Write the whole number as a fraction with the same denominator. For example, 3 − 2/5: write 3 as 15/5, then subtract: 15/5 − 2/5 = 13/5 = 2 3/5.
Q6. What is the most common mistake?
Subtracting both numerators and denominators separately. For example, writing 3/4 − 1/3 = 2/1 is wrong. You must find a common denominator first.
Q7. Is this method the same as adding unlike fractions?
The process is identical — find LCM, convert to like fractions, then perform the operation. The only difference is that you subtract instead of add in the final step.
Q8. What if the LCM is very large?
Large LCMs mean larger numbers to work with, but the method stays the same. Practice helps build speed. Always use LCM (not just the product of denominators) to keep numbers as small as possible.
Q9. Is this covered in the NCERT Class 5 textbook?
Yes. Subtracting unlike fractions is a core topic in the Fractions chapter of NCERT Class 5 Mathematics, immediately following addition of unlike fractions.
Related Topics
- Adding Unlike Fractions
- Fractions Revision (Grade 5)
- Adding Mixed Numbers
- Subtracting Mixed Numbers
- Multiplying Fractions
- Multiplying a Fraction by a Whole Number
- Fraction of a Number
- Reciprocal of a Fraction
- Dividing Fractions
- Fraction Word Problems (Grade 5)
- Proper, Improper and Mixed Fractions
- Comparing and Ordering Fractions (Grade 5)
