How to Subtract Multi Digit Numbers Step by Step with Borrowing and Solved Examples
The topic of Subtraction Operation On Multi Digit Numbers is a foundational arithmetic skill that every student needs for success in school and daily tasks. Mastering multi-digit subtraction prepares you for higher-level math, exams like Olympiads and NTSE, and practical situations like shopping or budgeting.
Understanding Subtraction Operation On Multi Digit Numbers
Subtraction is the process of finding the difference between two numbers. When working with multi-digit numbers, subtraction is performed column by column, starting from the rightmost digit. If the digit in the minuend (the number being subtracted from) is smaller than the digit in the subtrahend (the number being subtracted), you need to borrow from the next left column. This process is also called regrouping or borrowing.
Key terms in subtraction operation on multi digit numbers:
- Minuend: The number from which another number is subtracted.
- Subtrahend: The number that is to be subtracted.
- Difference: The answer you get after subtraction.
- Borrowing (Regrouping): Taking 1 from the next column when the top digit is smaller.
- Place value: The position (ones, tens, hundreds, etc.) of each digit in a number.
Step-by-Step Subtraction Algorithm
Here is how to perform subtraction operation on multi digit numbers:
- Write the numbers in columns, aligning the ones, tens, hundreds, and thousands.
- Start from the ones' column (rightmost digit).
- If the top digit is greater than or equal to the bottom digit, subtract directly.
- If the top digit is smaller, borrow 1 from the next left column (which becomes 10 in the current column), then subtract.
- Repeat the process for all columns, moving left.
- Continue until all columns are completed to find the difference.
This process is known as subtraction with borrowing or regrouping. Understanding place value is essential for this.
Worked Examples
Example 1: Subtraction without Borrowing
Subtract 324 from 567:
| Hundreds | Tens | Ones |
|---|---|---|
| 5 | 6 | 7 |
| -3 | -2 | -4 |
| 2 | 4 | 3 |
So, 567 - 324 = 243
Example 2: Subtraction With Borrowing
Subtract 247 from 503:
| Hundreds | Tens | Ones |
|---|---|---|
| 5 | 0 | 3 |
| -2 | -4 | -7 |
| 3 | 6 (borrow) | 6 |
- Ones: 3 - 7 → Can’t do, borrow 1 from tens (but tens is 0).
- So, borrow 1 from hundreds: 5 becomes 4, tens becomes 10.
- Now, tens: 10 becomes 9 after giving 1 to ones → ones is now 13.
- Ones: 13 - 7 = 6
- Tens: 9 - 4 = 5
- Hundreds: 4 - 2 = 2
So, 503 - 247 = 256
Example 3: Subtraction with Zeros and Consecutive Borrowing
Subtract 1489 from 3002:
- Ones: 2 - 9 → Borrow from tens (0): borrow from hundreds.
- After all borrowing:
- Thousands: 3 - 1 = 2
- Hundreds: 0 (borrowed to tens) - 4 = 5 (from borrowing it becomes 9 - 4)
- Tens: 9 - 8 = 1
- Ones: 12 - 9 = 3
So, 3002 - 1489 = 1513
Practice Problems
- 1) 4,521 - 2,178
- 2) 7,035 - 6,289
- 3) 8,000 - 4,567
- 4) 5,100 - 2,748
- 5) 3,020 - 1,555
- 6) 6,200 - 3,107
- 7) 4,600 - 4,098
Try to solve these using the borrowing/regrouping method. If stuck, review the steps above or use Vedantu’s practice worksheets for more help!
Common Mistakes to Avoid
- Not borrowing correctly when the top digit is smaller than the bottom digit.
- Misaligning columns (ones under ones, tens under tens, etc.).
- Forgetting to reduce the digit after borrowing from it.
- Rushing and making calculation errors in each column.
Real-World Applications
Subtraction operation on multi digit numbers is used often in daily life:
- Calculating change while shopping: ₹2,500 - ₹1,375 gives you ₹1,125 as the remaining amount.
- Finding the amount of time left: 12:00 – 9:35 = 2 hours 25 minutes.
- Comparing scores or results in exams, sports, or polls.
- Balancing household budgets or recording business expenses.
At Vedantu, we help make these everyday calculations easy and fun through interactive lessons and real-life scenarios.
In this topic, we explored how to perform Subtraction Operation On Multi Digit Numbers using clear steps, working with and without borrowing, and understanding place value. Practicing these skills helps you avoid common mistakes, solve word problems faster, and apply maths confidently in real situations. Keep learning and practicing with Vedantu for a clearer understanding!
Class 2 Maths basics | Place Value in Numbers | Addition and Subtraction in Algebra
FAQs on Subtraction Operation on Multi Digit Numbers with Regrouping Explained
1. What is subtraction of multi digit numbers?
Subtraction of multi digit numbers is the process of finding the difference between two numbers that have two or more digits. It involves subtracting digits place by place (ones, tens, hundreds, etc.).
- Write the numbers in column form.
- Align digits according to place value.
- Subtract starting from the ones place.
- Regroup (borrow) if needed.
2. How do you subtract multi digit numbers step by step?
To subtract multi digit numbers, align place values and subtract from right to left, regrouping when necessary.
- Step 1: Write numbers vertically, aligning place values.
- Step 2: Subtract digits in the ones place.
- Step 3: If the top digit is smaller, borrow 1 from the next place.
- Step 4: Continue subtracting tens, hundreds, and so on.
3. What is borrowing in subtraction?
Borrowing, also called regrouping, is when you take 1 from the next higher place value to subtract a larger digit from a smaller digit. For example, in 52 − 38:
- 2 is smaller than 8, so borrow 1 ten from 5 tens.
- 52 becomes 4 tens and 12 ones.
- 12 − 8 = 4 and 4 − 3 = 1.
4. Can you give an example of subtraction with regrouping?
Yes, subtraction with regrouping involves borrowing from the next place value to complete the subtraction. Example: 402 − 185.
- Borrow from hundreds to tens, and tens to ones.
- 12 − 5 = 7
- 9 − 8 = 1
- 3 − 1 = 2
5. What is the formula for subtraction?
The basic subtraction formula is Minuend − Subtrahend = Difference. In multi digit subtraction:
- Minuend: the number you subtract from.
- Subtrahend: the number being subtracted.
- Difference: the result.
6. Why do we subtract from right to left in multi digit subtraction?
We subtract from right to left because subtraction depends on place value and regrouping starts from the ones place. Starting from the right:
- Allows borrowing from the next higher place.
- Maintains correct place value alignment.
- Ensures accurate calculation.
7. How do you subtract multi digit numbers with zeros?
To subtract multi digit numbers with zeros, borrow from the nearest non-zero digit to the left. Example: 500 − 278.
- Borrow across zeros: 500 becomes 4 hundreds, 9 tens, and 10 ones.
- 10 − 8 = 2
- 9 − 7 = 2
- 4 − 2 = 2
8. What are common mistakes in multi digit subtraction?
Common mistakes in multi digit subtraction include errors in place value alignment and incorrect regrouping. Frequent errors are:
- Not lining up digits correctly.
- Forgetting to reduce the digit after borrowing.
- Subtracting larger from smaller without regrouping.
- Arithmetic errors in basic subtraction facts.
9. What is the difference between subtraction with and without regrouping?
Subtraction without regrouping occurs when each top digit is larger than the bottom digit, while subtraction with regrouping requires borrowing. Example without regrouping: 864 − 321 = 543. Example with regrouping: 432 − 198 = 234. Regrouping is needed when a digit in the minuend is smaller than the corresponding digit in the subtrahend.
10. How can you check if your subtraction answer is correct?
You can check a subtraction answer by using the inverse operation, which is addition. Add the difference to the subtrahend:
- If 745 − 289 = 456
- Check: 456 + 289 = 745
