Common Mistakes in Multi Digit Subtraction and How to Avoid Them
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 Step-by-Step Guide to Subtracting Multi Digit Numbers
1. How to do subtraction with multiple digits?
Multi-digit subtraction involves subtracting numbers with more than one digit. Start by aligning the numbers vertically, with the ones place aligned, then subtract column by column, starting from the right (ones place). If a digit in the top number is smaller than the digit below it, you need to borrow from the digit to its left.
2. How to subtract 3 digit numbers step by step?
To subtract three-digit numbers, follow these steps: 1. Align the numbers vertically by place value. 2. Subtract the digits in the ones column. 3. If the top digit is smaller, borrow 10 from the tens column and add it to the ones column. 4. Subtract the digits in the tens column. 5. If the top digit is smaller, borrow from the hundreds column. 6. Subtract the digits in the hundreds column.
3. What is an example of multiple subtraction?
Multiple subtraction involves subtracting more than one number from another. For example: 456 - 123 - 54 = 279. This can be done by subtracting numbers sequentially or combining all subtrahends first. Always remember the rules of place value and borrowing.
4. How to subtract 3 sets of numbers?
Subtracting three sets of numbers is similar to multiple subtractions. You would subtract the numbers one at a time. It's helpful to first work out the difference between the first two numbers, and then subtract the third number from that result. Remember to properly align the numbers based on their place values.
5. How do you subtract multi-digit numbers step by step?
Subtracting multi-digit numbers involves a series of steps. First, align the numbers vertically by their place values. Then, subtract each column, starting from the right (ones place). If a digit on top is smaller than the one below, you must borrow from the column to its left. Continue this process until you finish all columns. Remember, regrouping is key!
6. What is borrowing/regrouping in subtraction?
Borrowing, or regrouping, is a key technique in subtraction. When a digit in the top number (minuend) is smaller than the corresponding digit in the bottom number (subtrahend), you 'borrow' a ten from the next higher place value column to make the subtraction possible. For example, in subtracting 42-18, you borrow 1 ten from the tens column to make the ones digit a 12 (12-8 = 4).
7. How do you subtract when there are zeros in the minuend?
Subtracting with zeros in the minuend requires careful regrouping. If you have a zero in a column, you have to borrow from the next column to the left, but that column might also have a zero. You keep borrowing until you reach a non-zero digit. Then proceed with the subtraction.
8. What is a subtraction algorithm?
A subtraction algorithm is a step-by-step method for performing subtraction. The standard algorithm involves aligning numbers by place value, subtracting column by column, and using borrowing or regrouping when needed. Understanding the algorithm ensures consistent and accurate calculations.
9. How to avoid mistakes when subtracting multi-digit numbers?
To avoid mistakes, carefully align the numbers vertically by place value. Double-check your borrowing steps to ensure accuracy and write clearly. Practice regularly, and review your work to catch any errors.
10. Why is borrowing essential in subtraction, but not in addition?
Borrowing is needed in subtraction because you're taking away a quantity. If a digit in the top number is smaller than the one below, you need to increase its value by borrowing from a higher place value to make the subtraction possible. In addition, you combine quantities, so borrowing isn't necessary.
