Subtraction of Decimals
Subtraction of decimals follows the same method as whole-number subtraction, with one key rule: line up the decimal points. You subtract column by column from right to left, borrowing when necessary.
We subtract decimals when calculating change while shopping, finding the difference in measurements, or comparing scores. In Class 5, you will subtract decimals with different numbers of decimal places and solve real-life problems.
What is Subtraction of Decimals - Class 5 Maths (Decimals)?
Subtracting decimals means finding the difference between two decimal numbers.
Rule: Align the decimal points, add trailing zeros, subtract column by column from right to left.
Subtraction of Decimals Formula
Steps to subtract decimals:
- Write the larger number on top and the smaller number below, with decimal points aligned.
- Add trailing zeros so both numbers have the same number of decimal places.
- Subtract from the rightmost column to the left.
- Borrow from the next column when the top digit is smaller than the bottom digit.
- Place the decimal point in the answer directly below the decimal points above.
Align → Equalise → Subtract → Place decimal
Types and Properties
Types of decimal subtraction problems:
- Same decimal places: e.g., 8.75 - 3.42 = 5.33
- Different decimal places: e.g., 6.5 - 2.375 → 6.500 - 2.375 = 4.125
- Whole number - Decimal: e.g., 10 - 3.65 → 10.00 - 3.65 = 6.35
- With borrowing: e.g., 5.03 - 2.78 (requires multiple borrows)
- Word problems: Finding change, remaining distance, weight difference, etc.
Solved Examples
Example 1: Example 1: Same Decimal Places
Problem: Subtract 9.87 - 4.52.
Solution:
9.87
- 4.52
-----
5.35
Answer: 9.87 - 4.52 = 5.35
Example 2: Example 2: Different Decimal Places
Problem: Subtract 8.5 - 3.275.
Solution:
Step 1: Equalise: 8.500 - 3.275
8.500
- 3.275
------
5.225
Answer: 8.5 - 3.275 = 5.225
Example 3: Example 3: Whole Number - Decimal
Problem: Subtract 12 - 7.35.
Solution:
Step 1: Write 12 as 12.00.
12.00
- 7.35
------
4.65
Answer: 12 - 7.35 = 4.65
Example 4: Example 4: Subtraction with Borrowing
Problem: Subtract 6.03 - 2.78.
Solution:
Step 1: Hundredths: 3 - 8 (cannot, borrow). Tenths becomes -1. But tenths: 0 - 1 (cannot). Borrow from ones.
6.03
- 2.78
-----
3.25
Check: Hundredths: 13 - 8 = 5. Tenths: 9 - 7 = 2 (after borrows). Ones: 5 - 2 = 3.
Answer: 6.03 - 2.78 = 3.25
Example 5: Example 5: Subtracting from a Number with Trailing Zeros
Problem: Subtract 10.00 - 4.567.
Solution:
Step 1: Equalise: 10.000 - 4.567
10.000
- 4.567
-------
5.433
Answer: 10 - 4.567 = 5.433
Example 6: Example 6: Word Problem (Shopping Change)
Problem: Aman buys a cricket bat for Rs.475.50. He pays Rs.500. How much change does he get?
Solution:
500.00
- 475.50
-------
24.50
Answer: Aman gets Rs.24.50 as change.
Example 7: Example 7: Word Problem (Weight)
Problem: A watermelon weighs 5.2 kg. After cutting, the rind weighs 1.85 kg. What is the weight of the edible part?
Solution:
Step 1: Equalise: 5.20 - 1.85
5.20
- 1.85
-----
3.35
Answer: The edible part weighs 3.35 kg.
Example 8: Example 8: Word Problem (Distance)
Problem: Neha's school is 3.75 km from home. She has walked 2.3 km. How much further does she need to walk?
Solution:
Step 1: Equalise: 3.75 - 2.30
3.75
- 2.30
-----
1.45
Answer: Neha needs to walk 1.45 km more.
Example 9: Example 9: Word Problem (Temperature)
Problem: The morning temperature was 18.5°C. By evening, it dropped to 14.75°C. By how much did the temperature fall?
Solution:
Step 1: Equalise: 18.50 - 14.75
18.50
- 14.75
------
3.75
Answer: The temperature fell by 3.75°C.
Example 10: Example 10: Multi-step Problem
Problem: Priya has Rs.200. She buys a book for Rs.85.75 and a pen for Rs.32.50. How much money is left?
Solution:
Step 1: Total spent = 85.75 + 32.50 = 118.25
Step 2: Money left = 200.00 - 118.25 = 81.75
Answer: Priya has Rs.81.75 left.
Real-World Applications
Real-life uses of decimal subtraction:
- Shopping: Calculating change received after a purchase.
- Cooking: Finding how much more of an ingredient is needed (e.g., need 2.5 kg, have 1.75 kg).
- Travel: Subtracting distance covered from total distance to find remaining distance.
- Science: Finding temperature changes, differences in rainfall, etc.
- Finance: Calculating expenses left from a budget.
Key Points to Remember
- Always align the decimal points before subtracting.
- Add trailing zeros to equalise decimal places.
- Subtract from right to left, column by column.
- Borrow from the next column when the top digit is smaller than the bottom digit.
- The decimal point in the answer goes directly below the other decimal points.
- When subtracting from a whole number, write it with .00 (e.g., 15 becomes 15.00).
- Verify by adding: difference + subtrahend should equal the minuend.
Practice Problems
- Subtract 15.84 - 7.39.
- Subtract 9.5 - 4.625.
- Subtract 20 - 8.45.
- Subtract 7.002 - 3.568.
- Kavi has Rs.100. He buys a book for Rs.67.75. How much money is left?
- A bottle contains 2.5 litres of oil. Aditi uses 0.875 litres. How much oil remains?
- The height of a building is 12.6 metres. A tree next to it is 8.95 metres tall. What is the difference in height?
- Dev scored 9.75 in a quiz. Rahul scored 8.8. By how much did Dev beat Rahul?
Frequently Asked Questions
Q1. How do I subtract decimals?
Line up the decimal points, add trailing zeros so both numbers have the same decimal places, then subtract column by column from right to left. Place the decimal point in the answer directly below.
Q2. What if the top digit is smaller than the bottom digit?
Borrow 1 from the next column to the left, just like in whole-number subtraction. The top digit becomes 10 + that digit, and the column to the left decreases by 1.
Q3. How do I subtract a decimal from a whole number?
Write the whole number with a decimal point and trailing zeros. For example, 8 - 3.25: write 8 as 8.00, then subtract 8.00 - 3.25 = 4.75.
Q4. Can the answer of a subtraction be a decimal even if both numbers look like whole numbers?
If both numbers are actual whole numbers, the difference is a whole number. But if one is written as a decimal (like 10.00 - 4.567), the answer will be a decimal: 5.433.
Q5. How do I verify my answer?
Add the answer (difference) to the smaller number. If you get the larger number, your subtraction is correct. For example, 5.35 + 4.52 = 9.87 verifies that 9.87 - 4.52 = 5.35.
Q6. Is decimal subtraction harder than addition?
The method is the same (align, equalise, work right to left). The only extra step is borrowing, which some students find trickier. Practice with borrowing will make it easy.
Q7. What is a common mistake in decimal subtraction?
Not aligning decimal points. If you subtract 8.5 - 3.25 without equalising (thinking 85 - 325), you get the wrong answer. Always write 8.50 - 3.25 to avoid errors.
Q8. Can the answer have fewer decimal places than the original numbers?
Yes. For example, 5.75 - 2.25 = 3.50 = 3.5. The trailing zero can be dropped if it is the last digit after the decimal point.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Subtraction of decimals is part of the NCERT/CBSE Class 5 Maths curriculum under the Decimals chapter. It is tested alongside decimal addition in exams.
Related Topics
- Addition of Decimals
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Multiplication of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
