Subtraction With Regrouping

Subtraction with regrouping helps in understanding and performing subtractions easily using the concept of regrouping, which is also known as carrying or borrowing. It is an important skill to master, which forms the basis of arithmetic. Subtraction with regrouping can be performed by keeping the place value in mind. Let us learn more about this concept.

Subtraction with regrouping is a process of arranging two or more large numbers vertically to find the difference between the two given numbers. Regrouping is the process of making groups of tens when adding or subtracting two-digit numbers (or more) which is another name for carrying and borrowing. In subtraction with regrouping, we will encounter borrowing more often where we take away one number from the corresponding place value. Subtraction is mainly used when the bottom number is higher than the top number.

Subtraction with regrouping is considered extremely helpful in daily life such as when we are dealing with money like shopping, when we want to measure time like calculating the exact time from a different time zone, and when we want to measure distance. When we subtract two numbers, we use some terms which are used in the subtraction expression:

• Minuend: The number from which the other number is subtracted.
• Subtrahend: The number which is to be subtracted from the minuend.
• Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend - Subtrahend = Difference.

Let us look at an example: Find the difference between 8 and 6.

Therefore, 8 - 6 = 2.

Subtraction with regrouping is also known as subtraction with borrowing. When the minuend is smaller than the subtrahend, we use the regrouping method. While regrouping, we borrow 1 number from the preceding column to make the minuend bigger than the subtrahend. Here are the steps used while subtracting numbers with regrouping:

• Step 1: Arrange the numbers according to their place value in a vertical manner.
• Step 2: Start subtracting the digits at one's place. If the number in the bottom is higher than the top number, we will borrow 1 from the tens column which will be combined to the number at the one's place.
• Step 3: After giving 1 to the one's place, the number at the ten's place will reduce by one number. Now, subtract the numbers at the one's place.
• Step 4: We follow step 2 with the rest of the numbers in 2-digit and more numbers. As and when we borrow, we subtract the numbers simultaneously.
• Step 5: Subtract the last number to find the final difference.

2-digit subtraction with regrouping can be performed by using the steps mentioned above. The place value for 2-digit numbers is ones and tens. Let us look at an example and solve it along with the steps for a better understanding. Subtract 29 from 65.

Step 1: Arrange the numbers according to their place value with the greater number on top. So 5 and 9 are in the one's place and 2 and 6 are in the ten's place.

Step 2: We begin with the one's place. Since 5 is smaller than 9, we borrow 1 from the ten's place i.e. 6 which becomes 5.

Step 3: The 1 that is borrowed makes 5 as 15. Hence, 15 - 9 = 6.

Step 4: Once we have subtracted the one's place, move on to the ten's place. 5 - 2 = 3.

Hence, the difference between 65 and 29 is 36.

3-digit subtraction with regrouping is also performed in a similar manner as the one-digit and the 2-digit numbers. The place value for 3-digit numbers is hundreds, tens, and ones. Let us look at an example for a better understanding. Subtract 314 from 157.

Step 1: Arrange the numbers according to their place value with the greater number on top. So 4 and 7 are at the one's place, 1 and 5 are at the ten's place, and 3 and 1 are at the hundred's place.

Step 2: We begin with the one's place. Since 4 is smaller than 7, we borrow 1 from the ten's place i.e. 1 which reduces to 0.

Step 3: The 1 that is borrowed makes 4 as 14. Hence, 14 - 7 = 7.

Step 4: Follow step 2 again with the ten's and hundred's place by borrowing 1 from each of the numbers which makes it, 3 at the hundred's place will reduce to 2 and 0 at the ten's place makes it 10. Subtract all the numbers to find the difference.

Hence, the difference between 314 and 157 is 157.

4-digit subtraction with regrouping is performed in a similar manner as the one-digit, 2-digit, and 3-digit numbers. Since this is 4-digits, the place values are thousands, hundreds, tens, and ones. Let us look at an example, Subtract 3678 from 8162.

• Step 1: Arrange the numbers according to their place value. Start subtracting the digits at ones place. We can see that 8 is greater than 2. So, we will borrow 1 from the tens column which will make it 12. Now, 12 - 8 = 4 ones.
• Step 2: After giving 1 to the one's column in the previous step, 6 becomes 5. Now, let us subtract the digits at the tens place (5 - 7). Here, 7 is greater than 5, so we will borrow 1 from the hundreds column. This will make it 15. So,15 - 7 = 8 tens.
• Step 3: In step 2 we had given 1 to the tens column, so we are left with 0 at the hundreds place. To subtract the digits on the hundreds place, i.e., (0 - 6) we will borrow 1 from the thousands column. This will make it 10. So, 10 - 6 = 4 hundreds.
• Step 4: Now, let us subtract the digits at the thousands place. After giving 1 to the hundreds column, we have 7. So, 7 - 3 = 4.

Therefore, the difference between the two given numbers is 8162 - 3678 = 4484.

In order to solve subtraction of decimals with regrouping, follow the given steps:

• Step 1: Arrange the numbers according to their place value, with the decimal point.
• Step 2: Write zeroes in the places wherever the length of decimal numbers is not the same.
• Step 3: Now subtract the decimal numbers with the same steps used for the other digits and find the output to subtraction.

For example: Subtract 56.24 from 7.57.

Related Topics

Here are a few topics related to subtraction with regrouping, take a look. 

• Subtraction with Complex Numbers 
• Addition and Subtraction of Decimals
• Addition and Subtraction of Integers
• Addition With Regrouping

What is Subtraction With Regrouping?

Subtraction with regrouping is considered the process of arranging 2 or more numbers vertically to find out the difference between these two numbers. Regrouping or borrowing is the process of taking away a number from the next number placed in the next place value. Subtraction with regrouping is one of the most important aspects that we encounter in daily life as well.

What is the Subtraction Formula?

When we subtract two numbers or when subtraction numbers with regrouping, we use some terms which are used in the subtraction expression:

• Minuend: The number from which the other number is subtracted.
• Subtrahend: The number which is to be subtracted from the minuend.
• Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend - Subtrahend = Difference. For example: 9 - 2 = 7. 9 is the minuend, 2 is the subtrahend, and 7 is the difference.

What are the Steps to 2-Digit Subtraction With Regrouping?

2-digit subtraction with regrouping is done with 2-digit numbers with the place value of ones and tens. The steps to subtraction with regrouping is very simple, here they are:

• Arrange the numbers according to their place value in a vertical manner.
• Start with the one's place. If the number in the bottom is higher than the top number, borrow 1 from the tens column that gets combined to the one's place number. Subtract the number at the one's place.
• Since a number is borrowed from the ten's place, the number reduces. We follow step 2 with the rest of the numbers in 2-digit numbers. As and when we borrow, we subtract the numbers simultaneously.
• Subtract the last number to find the final difference.

What are the Steps to 3-Digit Subtraction With Regrouping?

3-digit subtraction with regrouping is done in a similar manner to the 2-digits. While subtracting 3-digits with regrouping, we consider 3 place values i.e. one's, ten's, and hundred's. During the process of subtraction, we borrow one number from the corresponding place value that is combined with the lower number. Here are the steps:

• Arrange the numbers according to their place value in a vertical manner.
• Start with the one's place. If the number in the bottom is higher than the top number, borrow 1 from the tens column that gets combined to the one's place number. Subtract the number at the one's place.
• Since a number is borrowed from the ten's place, the number reduces. We follow step 2 with the rest of the numbers in 3-digit numbers.
• Subtract the last number to find the final difference.

What are the Steps to 4-Digit Subtraction With Regrouping?

4-digit subtraction with regrouping is a similar process as used for 2-digit numbers and 3-digit numbers. Here the place values are one's, ten's, hundred's, and thousand's. The steps are as follows:

• Arrange the numbers according to their place value in a vertical manner.
• Start with the one's place. If the number in the bottom is higher than the top number, borrow 1 from the tens column that gets combined to the one's place number. Subtract the number at the one's place.
• Since a number is borrowed from the ten's place, the number reduces. We follow step 2 with the rest of the numbers in 4-digit numbers.
• Subtract the last number to find the final difference.

What are the Steps to Subtraction With Regrouping of Decimals?

In order to solve subtraction of decimals with regrouping, follow the given steps:

• Arrange the numbers according to their place value, with the decimal point.
• Write zeroes in the places wherever the length of decimal numbers is not the same.
• Now subtract the decimal numbers with the same steps used for the other digits and find the output to subtraction.