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102 LearnersLast updated on September 1, 2025
Subtraction of Numbers with Regrouping
The mathematical operation of finding the difference between two numbers, where borrowing or regrouping is needed, is known as subtraction with regrouping. This method helps in accurately solving problems involving whole numbers and decimals, ensuring correct arithmetic operations.
What is Subtraction of Numbers with Regrouping?
Subtraction with regrouping involves borrowing from a higher place value when the digit in the minuend is smaller than the digit in the subtrahend.
It requires adjusting the numbers by borrowing from a higher place value to perform the subtraction accurately.
There are three components involved in subtraction:
Minuend: The number from which we subtract.
Subtrahend: The number that is subtracted.
Difference: The result obtained after subtraction.
How to do Subtraction with Regrouping?
When performing subtraction with regrouping, students should follow these steps:
Borrow from a higher place value: If the top digit is smaller than the bottom digit, borrow from the next left digit.
Subtract column by column: Start from the rightmost column and move left, ensuring each column is correctly subtracted.
Check your work: After obtaining the difference, add the subtrahend to the difference to make sure it equals the minuend.
Methods to do Subtraction with Regrouping
The following are methods for subtraction of numbers with regrouping:
Method 1: Vertical Method
To apply the vertical method for subtraction with regrouping, follow these steps:
Step 1: Write the numbers vertically, aligning the place values.
Step 2: Beginning with the rightmost column, subtract each pair of digits. Borrow from the next left column if necessary.
Step 3: Write down the result of each subtraction as you move left.
Method 2: Number Line Method
When using the number line method, start from the minuend and count backward by the value of the subtrahend.
For example, if subtracting 54 from 123,
Solution: Start at 123 on the number line, and count back 54. The position you end at will be the difference.
Properties of Subtraction with Regrouping
Subtraction with regrouping has several important properties:
Subtraction is not commutative Changing the order of the numbers changes the result, i.e., A - B ≠ B - A.
Subtraction is not associative We cannot regroup the numbers in a different manner as we do with addition; changing the grouping changes the result.
(A − B) − C ≠ A − (B − C).
Subtraction involves borrowing When a digit in the minuend is smaller than the corresponding digit in the subtrahend, borrowing is necessary.
Subtracting zero from a number leaves the number unchanged
Subtracting zero from any number results in the same number: A - 0 = A.
Tips and Tricks for Subtraction with Regrouping
Tips and tricks can help students efficiently handle subtraction with regrouping. Here are some helpful tips:
Tip 1: Always pay attention to borrowing from the next left column when needed.
Tip 2: Double-check your results by adding the difference to the subtrahend to see if it equals the minuend.
Tip 3: For visual learners, using a number line can help in understanding the backward counting involved in subtraction.
Forgetting to borrow correctly
Students often forget to borrow or incorrectly borrow from the next left column. Always ensure you adjust the minuend correctly before subtracting.
Mistake 1
Misaligning place values
Ensure that digits are aligned according to their place values; misaligned numbers lead to incorrect results.
Mistake 2
Ignoring the need to regroup
Sometimes students proceed without noticing the need to borrow, which results in negative digits and incorrect answers.
Mistake 3
Not checking the final result
Always verify your answer by adding the difference to the subtrahend to ensure it matches the minuend.
Mistake 4
Overlooking zero as a place holder
In cases where zeros are present in the minuend, remember to treat them as placeholders and borrow from the next significant digit.
Mistake 5
Examples of Subtraction with Regrouping
Subtract 28 from 73
45
Problem 1
Use the vertical method: Write 73 and 28 vertically. Subtract 8 from 3; borrow from 7 to make it 13. The 7 becomes 6. 13 - 8 = 5, 6 - 2 = 4. The difference is 45.
Subtract 156 from 324
Explanation
168
Problem 2
Use the vertical method: Write 324 and 156 vertically. Subtract column by column; borrow where needed. 4 - 6 requires borrowing: 14 - 6 = 8, then 1 from the next column, 12 - 5 = 7, and 3 - 1 = 2. The difference is 168.
Subtract 487 from 1000
Explanation
513
Problem 3
Use the vertical method: Write 1000 and 487 vertically. Borrow across zeros, making it 10 - 7 = 3, 9 - 8 = 1, 9 - 4 = 5. The difference is 513.
Subtract 239 from 562
Explanation
323
Problem 4
Use the vertical method: Write 562 and 239 vertically. Subtract column by column; borrow where needed. 2 - 9 requires borrowing: 12 - 9 = 3, then 5 - 3 = 2, and 5 - 2 = 3. The difference is 323.
Subtract 75 from 200
Explanation
125
Yes, if the digits in the minuend are greater than the corresponding digits in the subtrahend, subtraction can occur without regrouping.
1.Is subtraction commutative?
2.What is regrouping?
3.What is the first step in subtraction with regrouping?
4.What methods are used for subtraction with regrouping?
Common Mistakes and How to Avoid Them in Subtraction with Regrouping
Subtraction with regrouping can be challenging, often leading to common mistakes. Being aware of these errors can help students avoid them.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
