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:
- Ones place: 4 + 5 = 9
- Tens place: 3 + 4 = 7
- 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:
1
2 7 6
- Write down 5 in the ones place of the answer.
- Carry over 1 to the tens place.
- 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:
- The 3 in the tens place becomes 2 (since we took 1).
- The 2 in the ones place becomes 12 (because we added 10 from the borrowed ten).
- 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:
- 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).
- 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).
- 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!
Frequently asked questions
How do I add two three-digit numbers?
Stack the numbers vertically with each digit aligned by place value (ones with ones, tens with tens, hundreds with hundreds). Add the ones column first; if the sum is 10 or more, write the ones digit and carry the tens digit to the next column. Add the tens column (including any carry); regroup if needed. Then add the hundreds column. Example: 247 + 386 — ones: 7+6=13, write 3 carry 1; tens: 1+4+8=13, write 3 carry 1; hundreds: 1+2+3=6. Answer: 633.
How do I subtract a three-digit number with borrowing?
Stack the numbers vertically aligned by place value. Start at the ones column; if the top digit is smaller than the bottom digit, borrow 1 from the tens column (which becomes a 10 in the ones column). Subtract. Move to the tens column, repeating the borrow if needed (this time from the hundreds). Then subtract the hundreds. Example: 503 − 247 — ones: 3 < 7, borrow from tens (but tens is 0, so borrow from hundreds first). After regrouping: 4 hundreds, 9 tens, 13 ones. Now subtract: 13−7=6, 9−4=5, 4−2=2. Answer: 256.
What does "regrouping" mean in addition and subtraction?
Regrouping is just trading between place-value columns. In addition, when a column sums to 10 or more, you regroup the 10 into the next column (this is "carrying"). In subtraction, when the top digit is smaller than the bottom, you regroup 1 from the next column to the right (this is "borrowing"). The key insight: 1 ten = 10 ones, 1 hundred = 10 tens, and so on. Every regrouping move is a 10-for-1 trade between adjacent columns.
How can I help my child stop making errors in three-digit subtraction?
Two changes usually fix the most common errors. First, re-introduce the column labels: write H | T | O at the top so the place value is impossible to lose track of. Second, teach the habit of estimating the answer FIRST by rounding both numbers to the nearest hundred — if 503 − 247 should land somewhere near 500 − 250 = 250, then a computed answer of 154 is obviously wrong and triggers a recheck. The estimate-first habit catches roughly 80% of column-arithmetic errors.
When should children master three-digit addition and subtraction?
In US Common Core curriculum, addition and subtraction of two-digit numbers within 100 is a Grade 1-2 standard, and addition and subtraction within 1,000 (three-digit) is a Grade 2-3 standard. Most learners reach fluency by mid-Grade 3 with regular practice. The benchmark to look for: can the child solve a three-digit problem with regrouping in under a minute, with the work written out clearly? If yes, they are ready to extend to four- and five-digit numbers and to start long multiplication.