Subtracting Mixed Numbers
Subtracting mixed numbers involves finding the difference between two quantities that have both a whole number part and a fraction part. In Class 5, students learn to handle cases where the fraction being subtracted is larger than the fraction it is subtracted from — requiring borrowing (regrouping) from the whole number.
This is one of the trickiest fraction operations in Class 5, but with practice, the steps become automatic.
Consider this problem: a rope is 5 1/4 metres long. You cut off 2 3/4 metres. How much is left? You need to subtract 3/4 from 1/4, but 1/4 is smaller than 3/4. This is where borrowing comes in — you take 1 from the whole number (making it 4 instead of 5) and convert that 1 into 4/4, giving you 5/4 to subtract from.
Borrowing in fractions works exactly like borrowing in whole number subtraction. When the ones digit is too small, you borrow from the tens. Here, when the fraction part is too small, you borrow from the whole number part.
Tip: If borrowing feels confusing, use the improper fraction method instead — it avoids borrowing entirely by converting everything to a single fraction first.
What is Subtracting Mixed Numbers - Class 5 Maths (Fractions)?
A mixed number has a whole part and a proper fraction part (e.g., 5 2/3).
Two methods for subtracting mixed numbers:
Method 1: Convert to Improper Fractions
- Convert both mixed numbers to improper fractions.
- Find the LCM of the denominators.
- Subtract the fractions.
- Convert the result back to a mixed number.
Method 2: Subtract Parts Separately (with Borrowing)
- Subtract the fractions. If the first fraction is smaller, borrow 1 from the whole number.
- Subtract the whole numbers.
- Combine.
Subtracting Mixed Numbers Formula
Method 1 (Improper Fractions):
Convert → Find LCM → Subtract → Simplify → Convert back
Borrowing Rule:
If the first fraction is smaller, borrow 1 from the whole number.
1 borrowed = denominator/denominator added to the fraction part.
Types and Properties
Case 1: No borrowing needed (first fraction is larger)
Example: 5 3/4 − 2 1/4 = 3 2/4 = 3 1/2. Simply subtract whole parts and fraction parts.
Case 2: Borrowing needed (first fraction is smaller)
Example: 5 1/4 − 2 3/4. Since 1/4 < 3/4, borrow 1 from 5 (making it 4) and add 4/4 to 1/4 to get 5/4. Then: 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2.
Case 3: Different denominators
Find LCM first, convert to like fractions, then subtract (with borrowing if needed).
Case 4: Subtracting from a whole number
Example: 7 − 2 3/5 = 6 5/5 − 2 3/5 = 4 2/5.
Solved Examples
Example 1: Example 1: No Borrowing Needed
Problem: Calculate 6 5/8 − 3 1/8.
Solution:
Step 1: Subtract whole numbers: 6 − 3 = 3.
Step 2: Subtract fractions: 5/8 − 1/8 = 4/8 = 1/2.
Step 3: Combine: 3 1/2.
Answer: 6 5/8 − 3 1/8 = 3 1/2
Example 2: Example 2: Borrowing Required
Problem: Calculate 5 1/6 − 2 5/6.
Solution:
Step 1: Compare fractions: 1/6 < 5/6. Need to borrow.
Step 2: Borrow 1 from 5: 5 1/6 becomes 4 7/6 (since 1 = 6/6, and 6/6 + 1/6 = 7/6).
Step 3: Subtract whole numbers: 4 − 2 = 2.
Step 4: Subtract fractions: 7/6 − 5/6 = 2/6 = 1/3.
Step 5: Combine: 2 1/3.
Answer: 5 1/6 − 2 5/6 = 2 1/3
Example 3: Example 3: Different Denominators, No Borrowing
Problem: Calculate 7 3/4 − 3 1/3.
Solution:
Step 1: LCM of 4 and 3 = 12.
Step 2: Convert fractions: 3/4 = 9/12 and 1/3 = 4/12.
Step 3: Subtract whole numbers: 7 − 3 = 4.
Step 4: Subtract fractions: 9/12 − 4/12 = 5/12.
Step 5: Combine: 4 5/12.
Answer: 7 3/4 − 3 1/3 = 4 5/12
Example 4: Example 4: Different Denominators, Borrowing Needed
Problem: Calculate 8 1/4 − 3 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: Compare: 3/12 < 8/12. Need to borrow.
Step 4: Borrow 1 from 8: 8 3/12 becomes 7 15/12 (since 12/12 + 3/12 = 15/12).
Step 5: Subtract: 7 15/12 − 3 8/12 = 4 7/12.
Answer: 8 1/4 − 3 2/3 = 4 7/12
Example 5: Example 5: Subtracting from a Whole Number
Problem: Calculate 9 − 4 3/5.
Solution:
Step 1: Write 9 as 8 5/5 (borrow 1 from 9).
Step 2: Subtract whole numbers: 8 − 4 = 4.
Step 3: Subtract fractions: 5/5 − 3/5 = 2/5.
Step 4: Combine: 4 2/5.
Answer: 9 − 4 3/5 = 4 2/5
Example 6: Example 6: Using Improper Fractions Method
Problem: Calculate 6 1/3 − 2 3/4 using improper fractions.
Solution:
Step 1: Convert: 6 1/3 = 19/3 and 2 3/4 = 11/4.
Step 2: LCM of 3 and 4 = 12.
Step 3: Convert: 19/3 = 76/12 and 11/4 = 33/12.
Step 4: Subtract: 76/12 − 33/12 = 43/12.
Step 5: Convert back: 43 ÷ 12 = 3 remainder 7. So 43/12 = 3 7/12.
Answer: 6 1/3 − 2 3/4 = 3 7/12
Example 7: Example 7: Word Problem — Fabric
Problem: Priya had 5 1/2 m of cloth. She used 2 3/4 m for a dress. How much cloth is left?
Solution:
Step 1: LCM of 2 and 4 = 4. Convert: 1/2 = 2/4.
Step 2: Compare: 2/4 < 3/4. Need to borrow.
Step 3: Borrow: 5 2/4 becomes 4 6/4.
Step 4: Subtract: 4 6/4 − 2 3/4 = 2 3/4.
Answer: 2 3/4 m of cloth is left.
Example 8: Example 8: Word Problem — Water
Problem: A bucket holds 8 1/3 litres. After Rahul pours out some water, 3 5/6 litres remain. How much did he pour out?
Solution:
Step 1: Water poured = 8 1/3 − 3 5/6.
Step 2: LCM of 3 and 6 = 6. Convert: 1/3 = 2/6.
Step 3: Compare: 2/6 < 5/6. Need to borrow.
Step 4: Borrow: 8 2/6 becomes 7 8/6.
Step 5: Subtract: 7 8/6 − 3 5/6 = 4 3/6 = 4 1/2.
Answer: Rahul poured out 4 1/2 litres.
Example 9: Example 9: Simplification Needed
Problem: Calculate 10 5/6 − 6 1/6.
Solution:
Step 1: Subtract whole numbers: 10 − 6 = 4.
Step 2: Subtract fractions: 5/6 − 1/6 = 4/6 = 2/3.
Step 3: Combine: 4 2/3.
Answer: 10 5/6 − 6 1/6 = 4 2/3
Example 10: Example 10: Word Problem — Distance
Problem: The distance from Aditi's house to school is 3 1/4 km. She has already walked 1 5/8 km. How much more does she need to walk?
Solution:
Step 1: Remaining = 3 1/4 − 1 5/8. LCM of 4 and 8 = 8. Convert: 1/4 = 2/8.
Step 2: Compare: 2/8 < 5/8. Need to borrow.
Step 3: Borrow: 3 2/8 becomes 2 10/8.
Step 4: Subtract: 2 10/8 − 1 5/8 = 1 5/8.
Answer: Aditi needs to walk 1 5/8 km more.
Real-World Applications
Where subtracting mixed numbers is used:
- Cooking: Finding how much more of an ingredient is needed
- Sewing: Calculating remaining fabric after cutting
- Distance: Finding how much further you need to travel
- Time: Calculating remaining time in hours and fractions
- Shopping: Determining how much weight or quantity is left after a purchase
Key Points to Remember
- To subtract mixed numbers, use either the improper fractions method or the separate parts method with borrowing.
- If the first fraction part is smaller than the second, borrow 1 from the whole number.
- Borrowing 1 means adding the denominator/denominator to the fraction part (e.g., borrow 1 = 4/4 when denominator is 4).
- When denominators are different, find the LCM first and convert to like fractions.
- To subtract from a whole number, write it as a mixed number with fraction = denominator/denominator.
- Always simplify the final answer.
- The improper fraction method avoids borrowing altogether — convert, subtract, convert back.
Practice Problems
- Calculate 7 5/6 − 3 1/6.
- Subtract 4 3/4 from 9 1/4 (borrowing required).
- Calculate 8 1/3 − 5 5/6.
- Dev had 6 1/2 litres of paint. He used 3 3/4 litres. How much is left?
- Subtract: 10 − 4 2/7.
- Neha ran 5 2/5 km. Meera ran 3 4/5 km. How much farther did Neha run?
- Calculate 12 1/6 − 7 3/4 using the improper fractions method.
- A rope is 15 1/3 m long. After cutting off 8 2/3 m, what length remains?
Frequently Asked Questions
Q1. What does borrowing mean when subtracting mixed numbers?
When the fraction you are subtracting is larger than the fraction you are subtracting from, you borrow 1 from the whole number. This 1 is converted to a fraction with the same denominator and added to the existing fraction part. For example, 5 1/4 becomes 4 5/4 after borrowing.
Q2. Which method is easier — improper fractions or borrowing?
The improper fractions method is more mechanical and avoids the borrowing step entirely. Many students find it easier because it follows a fixed sequence: convert, subtract, convert back. The borrowing method is quicker for simple numbers.
Q3. How do I subtract a mixed number from a whole number?
Borrow 1 from the whole number and write it as a fraction. For example, 7 − 3 2/5: write 7 as 6 5/5, then subtract: 6 5/5 − 3 2/5 = 3 3/5.
Q4. What if both fractions have different denominators?
Find the LCM of the denominators, convert both fractions to equivalent fractions with that denominator, and then subtract. If borrowing is needed, borrow using the common denominator.
Q5. Can the answer to a subtraction be a whole number?
Yes. For example, 5 3/4 − 2 3/4 = 3. When the fraction parts are equal, they cancel out, leaving only the whole number difference.
Q6. What is the most common mistake?
Forgetting to borrow when the first fraction is smaller. Students sometimes write 5 1/4 − 2 3/4 = 3 (-2/4), which is incorrect. Always check whether borrowing is needed before subtracting the fractions.
Q7. Should I always simplify the answer?
Yes. Check if the fraction part can be reduced. For example, if you get 4 4/6, simplify to 4 2/3.
Q8. How do I check my answer?
Add the answer to the smaller mixed number. If you get back the larger mixed number, your subtraction is correct. For example, if 8 1/3 − 3 2/3 = 4 2/3, check: 4 2/3 + 3 2/3 = 8 1/3 (after carrying over 4/3 = 1 1/3).
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Subtracting mixed numbers is part of the Fractions chapter in NCERT Class 5 Mathematics. Students practise both with like and unlike denominators, including borrowing.
Related Topics
- Adding Mixed Numbers
- Adding Unlike Fractions
- Fractions Revision (Grade 5)
- Subtracting Unlike Fractions
- 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)
