Subtraction With Regrouping

Subtraction is a fundamental mathematical operation used to determine the difference between two numbers, showing how much is left when one amount is taken away from another. The minus sign (-) represents subtraction. For instance, if you have 15 balloons and 6 float away, subtraction helps you figure out how many balloons remain: 15 – 6 = 9

Subtraction with regrouping is used to find the difference between two or more large numbers by arranging them vertically. In this method, we borrow 1 from the next highest place value if the minuend is smaller than the subtrahend. Regrouping, also known as borrowing, is the process of forming groups of ten while adding or subtracting two-digit numbers (or more). When the bottom number is greater than the top number, we subtract values place by place.

Subtraction with regrouping is useful in our daily life, such as when we are dealing with money like shopping, measuring time, or calculating distance. The essential terms related to the subtraction process are:

• Minuend: The number from which another number is subtracted.

• Subtrahend: The number which is subtracted from the minuend.

• Difference: The result obtained by subtracting the minuend from the subtrahend.

That is, Minuend - Subtrahend = Difference
 

In subtraction, when the subtrahend is greater than the corresponding digit in the minuend, we use the regrouping method to find the difference. Here are the certain steps we must follow when performing subtraction with borrowing:

Step 1: Vertically arrange the numerals based on their place value. 

Step 2:  At one's place, begin subtracting the numbers. We borrow 1 from the tens place and add it to the number at the one's place if the bottom number is greater than the top number. 

Step 3: After borrowing 1 from the tens place, the value in that place decreases by one. Add 10 to the one place, then subtract.

Step 4: If needed, repeat the borrowing process for the remaining numbers. Borrow from each place value and subtract it from right to left.  

Step 5: To find the final difference, subtract all the digits and write the answer.
 

Ones and tens are the place values for two-digit numerals. For a better understanding, let’s examine an example and solve it together with the stages. Subtract 29 from 75.

Step 1: Arrange the numbers by place value
Write the numbers vertically so that ones line up with ones, and tens with tens. Place the larger number on top:

  75
- 29
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----------

Step 2: Begin with the ones place
Compare the digits in the ones column: 5 (top) and 9 (bottom). Since 5 < 9, we cannot subtract without borrowing.

Borrowing process: Take 1 ten from the tens place of 75. This reduces the tens digit from 7 to 6.
 

Step 3: Adjust the ones digit
The borrowed 1 ten adds 10 to the ones place. So 5 becomes 15.

Now subtract the ones digits:

15 − 9 = 6
 

Step 4: Move to the tens place
After borrowing, the tens digits are 6 (top) and 2 (bottom). Subtract:

6 − 2 = 4

Write 4 in the tens place of your answer.

Therefore, 75 - 29 = 46.
 

Three-digit subtraction with regrouping follows the same method as one-digit and two-digit subtraction. In a three-digit number, the place values are hundreds, tens, and ones. Let’s go through an example to understand it better. Subtract 248 from 562.
 

Step 1: Arrange the numbers by place value.
Write the numbers vertically, aligning the digits according to their place values:

  562
- 248
----------
----------

The digits align as follows:

• Ones: 2 and 8
• Tens: 6 and 4
• Hundreds: 5 and 2

Step 2: Subtract the ones place (units).
Compare the digits in the ones place: 2 (top) and 8 (bottom). Since 2 is less than 8, borrowing is needed.

Step 3: Borrow from the tens place.
Take 1 ten from the tens digit of 6 (which reduces it to 5). The borrowed 1 ten adds 10 to the ones digit:
 

• Ones: 2 becomes 12
• Tens: 6 becomes 5
   

Step 4: Perform the subtraction in each place
 

• Ones: 12 - 8 = 4
• Tens: 5 - 4 = 1
• ​​​​​​​Hundreds: 5 - 2 = 3
   

Final difference = 314

Subtraction of 4-digit numbers with regrouping is done in the same way as with 1-digit, 2-digit, and 3-digit numbers. Since this involves 4 digits, the place values are thousands, hundreds, tens, and ones. Let’s look at an example: Subtract 4529 from 7384.

Step 1: Arrange the numbers by place value
Write the numbers vertically, with digits aligned according to place value:

  7 3 8 4
- 4 5 2 9
-------------
-------------
 

Start subtracting from the ones place: Compare 4 (top) and 9 (bottom). Since 4 < 9, we need to borrow.

Borrowing 1 ten from the tens place (which has 8) converts 4 → 14, and reduces the tens digit from 8 to 7.

Now subtract the ones digits: 14 − 9 = 5

Step 2: Subtract the tens place
After borrowing, the tens digits are 7 (top) and 2 (bottom). Since 7  ≥  2, no borrowing is needed here.

Subtract: 7 − 2 = 5

Step 3: Subtract the hundreds place
Compare hundreds digits: 3 (top) and 5 (bottom). Since 3 < 5, we must borrow.

Borrow 1 thousand from the thousands place (which has 7), reducing it to 6 and adding 10 hundreds to the hundreds place:

3 + 10 = 13
3 → 13

Now subtract hundreds digits: 13 − 5 = 8

Step 4: Subtract the thousands place
After borrowing, the thousands digits are 6 (top) and 4 (bottom).
Subtract: 6 − 4 = 2

So,

Ones: 14 − 9 = 5
Tens: 7 − 2 = 5
Hundreds: 13 − 5 = 8
Thousands: 6 − 4 = 2
 

Final answer: 7384 − 4529 = 2855

To solve subtraction of decimals with regrouping, follow these steps:

Step 1: Align the numbers according to their place values, ensuring the decimal points are in the line.

Step 2: If the decimal numbers have different lengths, add zeros where necessary to make them equal in length.

Step 3: Subtract the decimal numbers using the same steps as regular subtraction, applying regrouping if needed. 

For example: Subtract 42.68 from 75.3
 

Subtraction with regrouping involves borrowing from higher place values when the minuend digit is smaller than the subtrahend digit in the same column. Here are a few tips to help students develop confidence and accuracy in this fundamental skill:
 

• Establish understanding through decomposition exercises where students practice breaking numbers into flexible place value combinations before attempting regrouping algorithms.
   
• Utilize real-world money scenarios to make regrouping concrete, such as trading dollar bills for dimes and pennies when making change or purchases.
   
• Learn systematic column-by-column analysis to identify potential regrouping needs before beginning calculations, rather than discovering them mid-process.
   
• Implement scaffolded progression from small numbers to multi-digit problems, ensuring mastery at each level before advancing to more complex regrouping situations.
   
• Develop mental visualization techniques where students imagine the physical exchange of place value units, reinforcing the concept that regrouping maintains numerical equivalence while reorganizing digits.

Subtraction with regrouping is used in many real-life situations. Here are a few examples:
 

• Shopping and Budgeting: Imagine you have $50, and you buy groceries worth $38.75. To find out how much money you have left, you subtract: $50.00 – $38.75 = $11.25. Borrow 1 from the tenths place or ones place as necessary before subtracting the hundredths. Since 0 is smaller than 5 in the hundredths place, you need to regroup before subtracting.

• Time Calculation: If a train leaves at 10:45 AM and halts for 2 hours and 50 minutes, subtract the halt duration to find the arrival time: 10:45 AM – 2 hours 50 minutes = 7:55 AM. Here, regrouping is needed, since 45 minutes is smaller than 50 minutes.

• Cooking and Measurements: If a recipe requires 2.5 cups of flour, but you have only 1.75 cups, subtract to find how much more you need: 2.50 – 1.75 = 0.75 cups.
   
• Sports Scoring: Coaches and fans use subtraction with regrouping to calculate point leads during basketball games (84 - 67 = 17) to think about gameplay strategy and manage time. 
   
• Inventory Management: Store managers use subtraction with regrouping to calculate remaining inventory levels (603 - 248 = 355) to plan when to restock inventory and to ensure enough inventory level for customer demand.