3-Digit Subtraction

3-digit subtraction is the subtraction of numbers in which the minuend consists of 3 digits and the subtrahend can be of either 1, 2, or 3 digits. We know that subtraction is an operation in Math, that gives the difference between two numbers. The number from which we subtract is called the minuend and the number which is subtracted from the minuend is called the subtrahend. While addition of numbers can be done with any set of numbers, in subtraction, we need to remember that the minuend as a whole should be larger than the subtrahend. 3-digit subtraction can be done with regrouping or without regrouping depending upon the value of the digits. Let us learn more about 3-digit subtraction in this article.

In 3-digit subtraction, we need to subtract the given numbers after placing them correctly according to their place values and we need to ensure that the bigger number is placed in the upper row, while the smaller number is placed below it. After aligning them into columns of ones, tens and hundreds, we start the process of subtraction. We know that the number from which the other number is subtracted is called the minuend, and the number which is subtracted from the minuend is called the subtrahend. The result of the subtraction of the two given numbers is called their difference.
Mathematically, this can be expressed as:

Minuend - Subtrahend = Difference

Let us see the basic steps that explain how to do 3-digit subtraction.

• Step 1: Write the given numbers one below the other in such a way that the bigger number is placed up and the smaller number is placed below it. They should be correctly placed under the columns of ones, tens, and hundreds.
• Step 2: Start subtracting the numbers from the ones column, followed by the tens column and then the hundreds column.
• Step 3: After all the columns are subtracted, we get the difference of the given numbers.

3-digit subtraction without regrouping means subtracting a set of numbers without borrowing any number from the preceding digit. While subtracting 3-digit numbers, if all the digits in the minuend are bigger than the digits in the subtrahend, the subtraction can be easily done by subtracting each column one by one. Once all the columns are subtracted, the final answer is obtained. This is called subtraction without regrouping. In such a case, there is no regrouping or borrowing of numbers because all the digits of the minuend are bigger in value than the subtrahend. For example, let us subtract two numbers to understand this better. Let us subtract 342 from 754.

Let us understand 3-digit subtraction without regrouping using the following steps:

• Step 1: Subtract the numbers under the ones column. 4 - 2 = 2. Write the difference (2) in ones column.
• Step 2: Subtract the numbers under the tens column. 5 - 4 = 1. Write the difference (1) in the tens column.
• Step 3: Subtract the numbers under the hundreds column. 7 - 3 = 4. Write the difference (4) in the hundreds column. Hence, the difference between the given numbers is 412.

3-digit subtraction with regrouping means we need to borrow a number from the preceding digit. In subtraction, regrouping is also known as borrowing. When we subtract 3-digit numbers, sometimes, a digit in the upper row is smaller than the digit in the lower row. In this case, we borrow a number from the preceding column so that the smaller minuend becomes bigger than the subtrahend. This is known as regrouping or borrowing, For example, let us subtract 167 from 283.

Let us understand this three-digit subtraction with regrouping using the following steps:

• Step 1: Write the given numbers according to their place values, one below the other in such a way that 283 is placed up and 167 is placed below it. They should be correctly placed under the columns of ones, tens, and hundreds.
• Step 2: Start subtracting the numbers from the ones column. It can be seen that 3 is smaller than 7. So, let us borrow 1 from the tens column which will make it 13. This is known as borrowing or regrouping in subtraction. So, 13 - 7 = 6. Now, we will write the difference (6) under the ones column.
• Step 3: After giving 1 to the ones column in the previous step, the '8' in the tens column changes to 7. Now, let us subtract the digits at the tens place and write the difference under the tens column (7 - 6 = 1).
• Step 4: In the hundreds column, we will subtract 1 from 2 and write the difference (1) in the column. (2 - 1 = 1). Thus, after subtracting all the 3 digits, we get the difference as 116.

3-digit addition and subtraction is similar to 2-digit addition and subtraction.

When we add 3-digit numbers, we write the given numbers (addends) one below the other such that they are placed correctly under the columns of ones, tens, and hundreds. Then, we add each column starting from the right-hand side. After all the columns are added, we get the sum of the given numbers.

In a similar way, we subtract 3-digit numbers by writing the bigger number on top and the smaller number below it correctly. Then, we subtract each column one by one starting from the ones column and moving on to the tens column, and then the hundreds column. Once all the columns are subtracted, we get the difference of the numbers.

☛ Related Articles

• 2-Digit Addition
• 2-Digit Subtraction
• 2-Digit Multiplication
• 3-Digit Addition
• 3-Digit Multiplication
• 4-Digit Addition
• 4-Digit Subtraction
• Addition and Subtraction of Decimals
• Addition and Subtraction of Integers
• Subtraction With Regrouping
• Subtraction on Number Line

What is 3-Digit Subtraction in Math?

Three-digit subtraction is the subtraction of numbers in which the minuend consists of 3 digits and the subtrahend can be of either 1, 2, or 3 digits. In subtraction, we need to remember that the minuend as a whole should be larger than the subtrahend. We subtract 3-digit numbers column-wise, starting from the ones column, moving on to the tens column and then to the hundreds column. 3 digit subtraction can be done with regrouping or without regrouping depending upon the value of the digits.

What is 3-Digit Subtraction Without Regrouping?

3-digit subtraction without regrouping means we need not borrow any number when we subtract the given numbers. While subtracting 3-digit numbers, if all the digits in the minuend are bigger than the digits in the subtrahend, the subtraction can be easily done. We start subtracting the numbers in the ones column, followed by the tens column, and then the hundreds column. Once all the columns are subtracted, the final answer is obtained. This is called subtraction without regrouping. In such a case, there is no regrouping or borrowing of numbers because all the digits of the minuend are bigger in value than the subtrahend.

How to do 3-Digit Subtraction?

In 3-digit subtraction, we need to subtract the given numbers after placing them correctly according to their place values. We also need to ensure that the bigger number is placed in the upper row, while the smaller number is placed below it. After aligning them into columns of ones, tens and hundreds, we start the process of subtraction. We start subtracting the numbers in the ones column, then we move on to the tens column and then to the hundreds column. After the digits in all the columns are subtracted, we get the difference of the given numbers.

What is 3-Digit Subtraction With Borrowing?

3-digit subtraction with borrowing means we need to regroup the numbers in the minuend because they are smaller than the respective subtrahend. In subtraction, regrouping is also known as borrowing. When we subtract 3-digit numbers, sometimes, a digit in the upper row is smaller than the digit in the lower row. In this case, we borrow a number from the preceding column so that the smaller minuend becomes bigger than the subtrahend. This is known as regrouping or borrowing. For example, let us subtract 167 from 485.

• Step 1: After arranging the numbers according to their place value, we start subtracting the digits from ones place. We can see that 5 is smaller than 7. So, we will borrow 1 from the tens column which will make it 15. So, 15 - 7 = 8. This is known as regrouping or borrowing in subtraction. Now, we will write 8 under the ones column.
• Step 2: After giving 1 to the ones column in the previous step, the '8' in the tens column changes to 7. Now, let us subtract the digits at the tens place and write 1 under the tens column (7 - 6 = 1).
• Step 3: In the hundreds column, we will subtract 1 from 4 and write 3 in this column. (4 - 1 = 3). Thus, after subtracting all the columns, we get the difference as 318.

Is 3-Digit Subtraction with Regrouping the same as 3 Digit Subtraction With Borrowing?

Yes, 3-digit subtraction with regrouping means 3-digit subtraction with borrowing. Whenever a number in the minuend is smaller than the respective number in the subtrahend, this number is regrouped by borrowing 1 from the preceding column, so that it becomes larger than the number in the subtrahend and then it can be subtracted easily.

How to do 3-Digit Subtraction with Zeros?

In 3-digit subtraction, when there are zeros in the subtrahend, it can be easily subtracted. For example, 543 - 100 = 443. However, when there are zeros in the minuend, we need to regroup and borrow 1 from the preceding column and then subtract the given numbers. For example, let us subtract 500 - 237.

• After placing the numbers in order, we start from the ones column and we can see that 0 is smaller than 7.
• So, we will borrow 1 from the tens column which will convert the 0 to 10. So, 10 - 7 = 3.
• It should be noted here that when we had borrowed 1 from the tens column, the digit in the tens column was also 0, so this 0 had to borrow 1 from the hundreds column and then give 1 to the ones column.
• Now, getting back to the subtraction in the tens column, we know that this 0 had changed to 10 when it had borrowed 1, and after giving 1 to the ones column, it became 9. So, we will subtract 9 - 3 = 6.
• Now, let us move to the hundreds column. Since 5 had given 1 to the tens column, it becomes 4, and 4 - 2 = 2.
• After all the columns have been subtracted one by one, we get the difference as, 500 - 237 = 263.