Subtraction With Regrouping

Subtraction is a fundamental mathematical operation used to determine the difference between two numbers. It shows 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: It is the number from which another number is subtracted. 

• Subtrahend: 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: Write the numbers vertically according to their place value. Arrange the larger number on the top and the smaller number below. Thus, 75 will be on top and 29 will be below. 

Step 2: We start the subtraction from the one's place. Since the digit in the one's place (5) is less than 9, we borrow 1 ten from the tens place (7), and it turns to 6. 


Step 3: The borrowed 1 turns 5 into 15. 
Now, subtract them:
15 – 9 = 6 as a result.

Step 4: Move to the tens place after subtracting the ones place. 
Here, we subtract 2 from 6.
  6 - 2 = 4. 

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: According to the place values, numbers are arranged, placing the greater number on top. In this case, 562 is on top, and 248 is below it. The digits are aligned as follows. So, 2 and 8 are in the ones place, 6 and 4 are in the tens place, and 5 and 2 are in the hundreds place. 

Step 2: As 2 is smaller than 8, we borrow 1 from the tens place (which is 6), reducing it to 5.  
 

Step 3: The 1 that is borrowed makes 2 become 12. Hence, 12 – 8 = 4.
 

Step 4: Follow Step 2 again with the tens and hundreds place values by borrowing 1. The 5 in the tens place reduces to 4, and the 4 in the ones place becomes 14. Now, subtract all the numbers to find the difference. 

Hence, the difference between 562 and 248 is 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 according to their place values. Start by subtracting the digits in the one's place. Since 9 is greater than 4, we borrow 1 from the tens place, making it 14; then 14 – 9 = 5.

Step 2: Since we borrowed 1 in the previous step, the 8 in the tens place is reduced to 7. Now, subtract the digits in the tens place (7 – 2). Since 2 is smaller than 7, no borrowing is needed. So, 7 – 2 = 5 tens.

Step 3: Subtract the digits in the hundreds place (3 – 5). Since 5 is greater than 3, we borrow 1 from the thousand's place, making it 13. Now, 13 – 5 = 8 hundreds. 

Step 4: After borrowing 1 in the previous step, the 7 in the thousands place becomes 6. Now, subtract the thousands place digits: 6 – 4 = 2 thousands. 

Therefore, the difference between the two given numbers is 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 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

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 only have 1.75 cups, you subtract to find how much more you need:

2.50 – 1.75 = 0.75 cups 

Regrouping is needed when subtracting decimals.