Subtraction is nothing but deducting one number from another. It is basically the process of removing something from the group or collection. 3-digit subtraction is an operation which is used to calculate the difference between two numbers of 3- digits. To subtract numbers, we first arrange them in place value columns then subtract the digits under ones, tens and hundreds columns. 3-digit subtraction is done with regrouping or without regrouping depending upon the value of the digits.

In this topic, we will learn about 3-Digit Subtraction and methods of subtraction of 3-digit numbers with and without regrouping.

We can study more about the subtraction of 3-digit numbers in this math article.

Three-digit subtraction is the subtraction of numbers wherein the minuend includes three digits and the subtrahend may be of 1, 2, or three digits.

In the process of subtraction, the smaller number is always subtracted from the bigger number. The smaller range is referred to as minuend and the large range is referred to as subtrahend. The end result is referred to as the difference.

The following are basic steps for 3-digit subtraction.

Step 1: Write the given numbers one below the other so that the larger number is at the top and the smaller number is at the top. The larger and smaller are placed correctly under the ones, tens and hundreds columns.

Step 2: Start to subtract numbers from the ones column, followed by the tens column and then the hundreds column.

Step 3: After subtracting all the columns, find the difference of the given numbers.

We can understand this three-digit subtraction using the following steps:

Example -Subtract \(754 -342 \).

Step I: Arrange the numbers vertically.

Step II: First subtract the ones column \(4 – 2 = 2 \).

Step III: Now, subtract the tens column \(5 – 4 = 1 \).

Lastly, subtract the hundreds column \( 7-3 = 4 \).

Therefore,\(754 – 342= 412 \) .

## 3-Digit Subtraction Without Regrouping

In 3-Digit Subtraction Without Regrouping , the numbers are written one below the other. When subtracting a 3 digit number, we first subtract one digit first, then tens digit and finally the hundreds digit.

We can understand this three-digit subtraction without regrouping using the following steps:

Example -Subtract 769 -245.

Step I: Arrange the numbers vertically.

Step II: First subtract the ones column \(9 – 5 = 4 \).

Step III: Now, subtract the tens column \( 6 – 4 = 2\).

Lastly, subtract the hundreds column \(7 – 2 = 5 \).

Therefore, \(769 – 245= 524 \).

## 3-Digit Subtraction With Regrouping

Regrouping in subtraction is used when one or more digits in the subtrahend are larger than the corresponding digits in the minuend.

For doing this, 1 is borrowed from the immediate next column on the left and regroups the numbers. It increases the value of the minuend. This makes us carry out the subtraction.

We will use the terms 1 ten = 10 ones and 1 hundred = 10 tens in the following steps.

Step 1: First place the numbers vertically and align the place values with the minuend at the top and the subtrahend below.

Step 2: Next, we focus on the tens column. Because we regroup 1 ten as 10 ones into the ones column, the value in the tens place will reduce by 1. This means we decrease 1 from 2. Thus, we are left with 1 in the tens column.

We can understand this three-digit subtraction with regrouping using the following steps:

Example – Subtract \( 463 -174 \)

Step I: First the numbers are vertically arranged.

Step II: We subtract the ones column. Because, 4 > 3 and in that case we cannot subtract 4 from 3. So, we regroup 6 tens and 3 ones. Now, \(6 tens + 3 ones = 5 tens and 13 ones \). \(13 – 4 = 9 ones \)

Step III: We subtract the tens column. Because, 1 ten is regrouped by ones column, so we are left with \( 6 – 1 = 5 tens \). We cannot subtract 8 from 7. So, we regroup 4 hundreds and 5 tens. Now, \( 4 hundreds + 5 tens = 4 hundreds and 15 tens\). \( 15 – 7 = 8 tens \).

Step IV: Subtract the hundreds column. \(3 – 1 = 2 hundreds \).

Therefore, \(463 -174=289 \).

Learn about Addition and Subtraction of Algebraic Expressions

## Solved example

**Ex-1 :** Subtract the 3-digit numbers: \(699 – 354 \).

**A2: **Let us place the numbers one below the other and subtract them.

Step 1: Subtract the numbers under the ones column. \(9 – 4 = 5 \). Write the difference (5) in ones column.

Step 2: Subtract the numbers under the tens column.\( 9 – 5 = 4\). Write the difference (4) in the tens column.

Step 3: Subtract the numbers under the hundreds column. \(6 – 3 = 3 \)Write the difference (3) in the hundreds column.This was three-digit subtraction without regrouping and the difference between the given numbers is 543.

**Ex-2:** Find the difference between the 3-digit numbers: \(450 – 178\). ** A1: **Let us subtract 178 from 450.

**Step 1:** Start subtracting the numbers under the ones column. We can see that 0 is less than 8. So, let us borrow 1 from the tens column which will make it 10. Now,\( 10 – 8 = 2\). Write the difference (2) in ones column.

**Step 2:** Moving on to the tens column, we know that after giving 1 to the ones column in the previous step, the ‘5’ in the tens column changes to 4. But 4 is again smaller than 7. So, let us borrow 1 from the hundreds column, which will make it 14. Now,\( 14 – 7 = 7 \). We will write the difference (7) in the tens column.

**Step 3:** Now, let us subtract the numbers under the hundreds column. Since 1 was given to the tens column, the 4 ” in the hundreds column changes to 3. Now,\( 3 – 1 = 2\), so we will write the difference (2) in the hundreds column. Thus, after subtracting all the 3 digits, we get the difference as 272.

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## 3-Digit Subtraction FAQs:

**Q.1How is subtracting from a 3-digit number?**

**Ans.1 **In 3-digit subtraction, when there are zeros in the subtrahend, it can be subtracted easily. For example,\( 643 – 100 = 543 \). If there are zeros in the minuend, we require to regroup and borrow 1 from the preceding column and then subtract the given numbers.

**Q.2What are the rules for subtracting numbers?**

**Ans.2 **the subtraction of integers is written as addition of the opposite number. To subtract two integers, the subtraction expression can be written as the first number plus the opposite of the second number.

**Q.3What are the 3 parts of subtraction?**

**Ans.3 **the 3 parts of subtraction are minuend, subtrahend, and difference Example- In the subtraction problem,\( 8 – 3 = 5 \), the number 8 is the minuend, the number 3 is the subtrahend and the number 5 is the difference.

**Q.4Is 3-Digit Subtraction with Regrouping the same as 3 Digit Subtraction With Borrowing?**

**Ans.4 **Yes.3-digit subtraction with regrouping and as 3 Digit Subtraction With Borrowing are the same.

**Q.5What is 3-Digit Subtraction Without Regrouping?**

**Ans.5 **To subtract 3-digit numbers, the numbers are mentioned one below the other. During subtracting 3 dig