Subtraction by Regrouping
Last Updated : 25 Jun, 2024
Subtraction by Regrouping commonly referred to as 'borrowing' or 'trading'. It helps students to handle subtraction operations when the digit on the top of the column is less than the digit below it for multi-digit numbers. This method is essential when the digit in the minuend (the number you are subtracting from) is smaller than the digit in the subtrahend (the number you are subtracting).
Imagine you have 32 and you need to subtract 15. You start with the one's place: 2 is smaller than 5, so you can't subtract 5 from 2. This is where regrouping comes into play. You borrow 1 ten from the tens place, turning the 3 into a 2 and adding 10 to the 2 in the ones place, making it 12. Now you can subtract 5 from 12, and then subtract the remaining tens.
This article provides insight into how to do subtraction with regrouping, how it works, and includes solved examples.
What is Subtraction?
Subtraction is one of the basic operations in mathematics, used to find the difference between two numbers. It tells us how much remains when one quantity is taken away from another. The symbol for subtraction is the minus sign (-).
For example, if you have 10 apples and you give away 3, subtraction helps you find out how many apples are left: 10 − 3 = 7.
So, you would have 7 apples remaining.
What is Subtraction by Regrouping?
Subtraction by regrouping is the process which is used where we are subtracting two numbers and if the digit in the minuend or first number is less than the digit at the subtrahend or second number at any particular place value. This makes the subtraction impossible and it calls for borrowing from the next higher place value column to make the necessary subtraction.
The borrowed value is then added to the smaller digit, allowing for the subtraction to be completed correctly.
Steps for Subtraction by Regrouping
Subtraction by regrouping involves a systematic approach to ensure accuracy. Here are the detailed steps:
Step 1: Write the larger number (minuend) above the smaller number (subtrahend), ensuring that the digits are aligned by place value (ones under ones, tens under tens, etc.).
Step 2: Begin the subtraction from the rightmost column (the ones place). If the digit in the minuend is smaller than the digit in the subtrahend, you need to regroup.
Step 3: Borrow 1 from the next left column. For example, if you need to subtract 6 from 4 in the ones place, you borrow 1 ten from the tens place. This changes the 4 to 14 in the ones place and reduces the tens place by 1.
Step 4: After regrouping, subtract the digits in each column.
Step 5: Continue the process for each column from right to left.
Examples of Subtraction by Regrouping
Here are a few examples of Subtraction by Regrouping:
Example with Two-Digits
Example: Subtract 47 from 85.
Write the numbers vertically:
85
-47
Start from the rightmost column: 5 - 7 (Regroup by borrowing 1 from the tens place)
Adjusted digits: 15 - 7 = 8
Subtract tens place: 7 - 4 = 3
Final answer: 38
Example with Three-Digits
Example: Subtract 234 from 567.
Write the numbers vertically:
567
-234
Start from the rightmost column: 7 - 4 = 3 (No regrouping needed)
Tens place: 6 - 3 = 3 (No regrouping needed)
Hundreds place: 5 - 2 = 3
Final answer: 333
Example with Four-Digits
Example: Subtract 3456 from 7890.
Write the numbers vertically:
7890
-3456
Ones place: 0 - 6 (Regroup by borrowing 1 from the tens place)
Adjusted digits: 10 - 6 = 4
Tens place: 8 - 5 = 3
Hundreds place: 9 - 4 = 5
Thousands place: 7 - 3 = 4
Final answer: 4434
Subtraction of Decimals with Regrouping
Subtracting decimals with regrouping is like subtracting whole numbers but it has got to do with the decimal points in that the decimal points in both quantities subtracted must be aligned. Here are the steps:
- Align the Decimal Points: Write the numbers vertically, ensuring that the decimal points are aligned.
- Regroup if Necessary: Start from the rightmost decimal place. If the top digit is smaller, regroup from the next higher place value column.
- Perform Subtraction: Subtract each column, moving from right to left, and ensure the decimal point in the answer is aligned correctly.
Let's consider an example for better understanding.
Example: Subtract 12.34 from 45.67.
Write the numbers vertically:
45.67
-12.34
Start from the rightmost decimal place: 7 - 4 = 3 (No regrouping needed)
Next decimal place: 6 - 3 = 3 (No regrouping needed)
Ones place: 5 - 2 = 3 (No regrouping needed)
Tens place: 4 - 1 = 3
Final answer: 33.33
Conclusion
Subtraction by regrouping is an important skill that helps us solve subtraction problems when the numbers are tricky. By borrowing from a higher place value, we can make sure we can subtract even when the top number is smaller than the bottom number.
This method might seem a bit complicated at first, but with practice, it becomes much easier. It's used in everyday tasks, like handling money and measuring things, making it a useful tool to know.
Read More,
Practice Problems on Subtraction by Regrouping
Problems for Subtraction by Regrouping |
| 752−486 | 500−236 |
| 613−297 | 634−298 |
| 840−563 | 789−357 |
| 725−459 | 903−587 |
| 981−654 | 432−178 |
| 537−298 | 620−483 |
| 402−178 | 754−495 |
| 860−594 | 810−672 |
| 731−492 | 970−453 |
| 948−679 | 614−325 |
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