Three-digit numbers contain hundreds, tens, and ones places, making them perfect for building strong arithmetic skills. Whether adding or subtracting, the key is working with each place value systematically.

Addition of Three-Digit Numbers

Simple Addition (No Regrouping)

Example: 234 + 145
Step-by-Step Solution:

1. Ones place: 4 + 5 = 9
2. Tens place: 3 + 4 = 7
3. Hundreds place: 2 + 1 = 3
   Final Sum: 234 + 145 = 379

Adding Three-Digit Numbers with Regrouping (Carrying Over)

Let’s break down the addition of 276 + 189 step by step, carefully applying regrouping (also called carrying over) where necessary.

Step 1: Write the Numbers Vertically

First, align both numbers by their place values (hundreds, tens, and ones):

  2 7 6  
+ 1 8 9  
---------  

Step 2: Add the Ones Place (6 + 9)

• 6 (from 276) + 9 (from 189) = 15
• Since 15 is a two-digit number, we:
  • Write down 5 in the ones place of the answer.
  • Carry over 1 to the tens place.

    1  
  2 7 6  
+ 1 8 9  
---------  
      5  

Step 3: Add the Tens Place (7 + 8 + Carried-Over 1)

• 7 (from 276) + 8 (from 189) = 15
• Add the carried-over 1 → 15 + 1 = 16
• Again, since 16 is a two-digit number, we:
  • Write down 6 in the tens place.
  • Carry over 1 to the hundreds place.

  1 1  
  2 7 6  
+ 1 8 9  
---------  
    6 5  

Step 4: Add the Hundreds Place (2 + 1 + Carried-Over 1)

• 2 (from 276) + 1 (from 189) = 3
• Add the carried-over 1 → 3 + 1 = 4
• Write down 4 in the hundreds place.

  1 1  
  2 7 6  
+ 1 8 9  
---------  
  4 6 5  

Final Answer:

276 + 189 = 465

Verification (Checking the Answer)

To ensure our addition is correct, we can subtract one of the numbers from the sum to see if we get the other number:

• 465 – 276 = 189 (✓ Correct)
• 465 – 189 = 276 (✓ Correct)

Since both subtractions return the original numbers, our addition is verified.

Adding three-digit numbers with regrouping ensures accurate calculations, especially when digits in a column add up to 10 or more. By carefully carrying over excess values, we maintain correct place values and arrive at the right sum.

Subtraction of Three-Digit Numbers

Subtracting three-digit numbers follows a structured method where we subtract each digit column by column, starting from the ones place. If the top digit is smaller than the bottom digit, we borrow from the next higher place value.

Example 1: Subtracting Without Borrowing (Initially)

Step 1: Write the Numbers Vertically

Align the digits by place value (hundreds, tens, and ones):

  5 3 2  
- 2 1 4  
---------  

Step 2: Subtract the Ones Place (2 – 4)

• Problem: The top digit (2) is smaller than the bottom digit (4).
• Solution: We must borrow 1 from the tens place.

How Borrowing Works:

1. The 3 in the tens place becomes 2 (since we took 1).
2. The 2 in the ones place becomes 12 (because we added 10 from the borrowed ten).
3. Now, subtract: 12 – 4 = 8

  5 2 12  
- 2 1  4  
---------  
        8  

Step 3: Subtract the Tens Place (2 – 1)

• After borrowing, the tens digit is now 2.
• Subtract: 2 – 1 = 1

  5 2 12  
- 2 1  4  
---------  
     1 8  

Step 4: Subtract the Hundreds Place (5 – 2)

• Subtract normally: 5 – 2 = 3

  5 2 12  
- 2 1  4  
---------  
  3 1 8  

Final Answer:

532 – 214 = 318

Example 2: Subtracting Three-Digit Numbers with Multiple Regrouping

Let’s explore a more challenging subtraction problem: 405 – 178. This example requires two levels of regrouping because we encounter a zero in the tens place, which forces us to borrow from the hundreds place first.

Step 1: Write the Numbers Vertically

Align the digits properly by their place values:

  4 0 5  
- 1 7 8  
---------  

Step 2: Subtract the Ones Place (5 – 8)

• Problem: The top digit (5) is smaller than the bottom digit (8).
• Solution: We need to borrow 1 from the tens place, but the tens digit is 0, which means we must first borrow from the hundreds place.

How Double Regrouping Works:

1. Borrow 1 from the hundreds place:
   • The 4 in the hundreds place becomes 3.
   • The 0 in the tens place becomes 10 (since we added 10 from the borrowed hundred).
2. Now, borrow 1 from the tens place for the ones place:
   • The 10 in the tens place becomes 9.
   • The 5 in the ones place becomes 15 (since we added 10 from the borrowed ten).
3. Subtract the ones place:
   • 15 – 8 = 7

  3 9 15  
- 1  7  8  
---------  
        7  

Step 3: Subtract the Tens Place (9 – 7)

• After regrouping, the tens digit is now 9.
• Subtract normally: 9 – 7 = 2

  3 9 15  
- 1  7  8  
---------  
     2 7  

Step 4: Subtract the Hundreds Place (3 – 1)

• Subtract normally: 3 – 1 = 2

  3 9 15  
- 1  7  8  
---------  
  2 2 7  

Final Answer:

405 – 178 = 227

Subtraction is not just about taking away—it’s about understanding numbers and their relationships. With patience and practice, even tricky problems become simple!