Subtraction of Decimals
If you have Rs. 50.00 and you spend Rs. 32.75 on a book, how much money do you have left? You need to subtract: 50.00 − 32.75 = 17.25. This is subtraction of decimals.
Subtracting decimals follows the same rules as subtracting whole numbers. The most important step is to line up the decimal points so that you subtract digits with the same place value.
In Class 6 NCERT Maths, you will learn how to subtract decimal numbers using the column method, including borrowing when needed.
What is Subtraction of Decimals - Grade 6 Maths (Decimals)?
Definition: Subtraction of decimals means finding the difference between two decimal numbers.
Golden rule:
Align the decimal points, then 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, lining up the decimal points.
- If the numbers have different numbers of decimal places, add trailing zeros to make them the same length.
- Subtract column by column from right to left.
- If a digit on top is smaller than the digit below, borrow from the next column (just like whole number subtraction).
- Place the decimal point in the answer directly below the other decimal points.
Types and Properties
Cases in decimal subtraction:
- Same decimal places: 8.75 − 3.42 — straightforward subtraction.
- Different decimal places: 9.5 − 3.28 — write 9.5 as 9.50, then subtract.
- Subtracting from a whole number: 15 − 3.45 — write 15 as 15.00, then subtract.
- Subtraction with borrowing: 6.32 − 2.85 — need to borrow because 2 < 5 in hundredths place.
Solved Examples
Example 1: Subtracting Decimals (Same Places)
Problem: Subtract 8.75 − 3.42.
Solution:
8.75
− 3.42
------
5.33
Answer: 5.33
Example 2: Subtracting Decimals (Different Places)
Problem: Subtract 7.6 − 2.35.
Solution:
Write 7.6 as 7.60:
7.60
− 2.35
------
5.25
Answer: 5.25
Example 3: Subtracting from a Whole Number
Problem: Subtract 10 − 3.45.
Solution:
Write 10 as 10.00:
10.00
− 3.45
------
6.55
Answer: 6.55
Example 4: Subtraction with Borrowing
Problem: Subtract 5.23 − 2.68.
Solution:
5.23
− 2.68
------
Hundredths: 3 − 8. Cannot do. Borrow 1 from tenths. 13 − 8 = 5.
Tenths: 1 − 6 (after lending 1, 2 became 1). Cannot do. Borrow 1 from ones. 11 − 6 = 5.
Ones: 4 − 2 = 2.
Answer: 2.55
Example 5: Money Problem
Problem: Rahul had Rs. 500. He spent Rs. 345.50 on shoes. How much money does he have left?
Solution:
500.00
− 345.50
-------
154.50
Answer: Rahul has Rs. 154.50 left.
Example 6: Length Problem
Problem: A rope is 8.5 m long. A piece of 3.75 m is cut off. Find the remaining length.
Solution:
8.50 − 3.75 = 4.75 m
Answer: Remaining length = 4.75 m.
Example 7: Weight Problem
Problem: A bag weighs 12.4 kg. After removing some items, it weighs 8.65 kg. What is the weight of the removed items?
Solution:
12.40 − 8.65 = 3.75 kg
Answer: The removed items weigh 3.75 kg.
Example 8: Subtracting Decimals Less Than 1
Problem: Subtract 0.8 − 0.35.
Solution:
Write 0.8 as 0.80:
0.80
− 0.35
------
0.45
Answer: 0.45
Example 9: Temperature Problem
Problem: The temperature at noon was 38.5°C and in the evening it was 32.8°C. Find the drop in temperature.
Solution:
38.5 − 32.8 = 5.7°C
Answer: The temperature dropped by 5.7°C.
Example 10: Subtracting Resulting in a Whole Number
Problem: Subtract 9.75 − 4.75.
Solution:
9.75 − 4.75 = 5.00 = 5
Answer: 5
Real-World Applications
Where subtraction of decimals is used:
- Shopping: Finding change after paying for items.
- Measurement: Finding the difference in lengths, weights, or volumes.
- Banking: Calculating balance after a withdrawal.
- Sports: Finding the time difference between two runners.
- Cooking: Finding how much more of an ingredient is needed.
Key Points to Remember
- Always line up the decimal points before subtracting.
- Add trailing zeros if the numbers have different decimal places.
- Subtract from right to 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 other decimal points.
- When subtracting from a whole number, write it with a decimal point and zeros (e.g., 7 = 7.00).
- The result can be a whole number if the decimal parts cancel out.
Practice Problems
- Subtract: 9.63 − 4.21.
- Subtract: 8.5 − 3.78.
- Subtract: 20 − 7.65.
- Subtract: 15.02 − 9.87.
- A bottle holds 2 litres of water. After pouring out 0.75 litres, how much is left?
- Subtract: 100 − 43.85.
Frequently Asked Questions
Q1. How do you subtract decimals?
Line up the decimal points so that digits with the same place value are in the same column. Add trailing zeros if needed. Subtract from right to left, borrowing when needed. Place the decimal point directly below.
Q2. What is borrowing in decimal subtraction?
When a digit on top is smaller than the digit below, you borrow 1 from the column to the left (just like in whole number subtraction). The borrowed 1 becomes 10 in the current column.
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 becomes 8.00. Then subtract as usual.
Q4. Why do we add trailing zeros?
Trailing zeros make both numbers have the same number of decimal places. This makes it easier to subtract column by column. Adding zeros does not change the value: 5.3 = 5.30.
Q5. Can the answer be a whole number?
Yes. If both numbers have the same decimal part, the difference is a whole number. For example, 7.25 − 3.25 = 4.00 = 4.
Q6. Is subtracting decimals the same as subtracting fractions?
Decimals are a type of fraction (with denominators of 10, 100, etc.). Subtracting decimals and subtracting equivalent fractions give the same result, but the decimal method is usually quicker.
