Carrying (or regrouping) is a fundamental math technique used when adding numbers where the sum of digits in a column equals 10 or more. The extra value is moved (“carried”) to the next higher place value to ensure accurate calculation.

Why Is Carrying Important?

• Enables accurate addition of large numbers
• Builds foundation for multi-digit arithmetic
• Essential for real-world applications like handling money, measurements, and data

Let’s break down the problem 67 + 58 step-by-step to fully understand how carrying works in two-digit addition.

Detailed Step-by-Step Solution for Two-Digit Numbers

Problem: 67 + 58

Step 1: Write the Numbers Vertically

First, we align the numbers by place value to make addition easier.

Step 2: Add the Ones Place (7 + 8)

• Calculation: 7 (from 67) + 8 (from 58) = 15
• What happens:
  • The sum 15 is 10 + 5
  • We write 5 in the ones place of our answer
  • We carry over 1 (representing 10) to the tens place

Step 3: Add the Tens Place (6 + 5 + Carry)

Now we add:

• 6 (from 67)
• 5 (from 58)
• 1 (that we carried over)
• Calculation: 6 + 5 + 1 = 12
• We write 12 in the tens place (which is actually 120)

Step 4: Final Answer

The complete addition gives us 125

Why This Works: Understanding Place Value

Let’s visualize the place values:

Number	Tens	Ones
67	6	7
58	5	8
Total	11	15

But we can’t have:

• 15 in the ones place (should be <10)
• 11 in the tens place (should be <10)

So we regroup:

1. From ones place: 15 = 10 + 5 → carry 10 to tens place
2. Now we have:
   • Tens: 11 + 1 (from the carry) = 12
   • Ones: 5

Final number: 12 tens and 5 ones = 125

Detailed Step-by-Step Solution for Three-Digit Numbers

Detailed Breakdown: 276 + 389

1. Adding the Ones Place (6 + 9)

• Calculation: 6 + 9 = 15
• Action:
  • Write 5 in the ones place of the answer
  • Carry over 1 to the tens place (since 15 = 10 + 5)

2. Adding the Tens Place (7 + 8 + Carry)

• Calculation: 7 + 8 + 1 (carried) = 16
• Action:
  • Write 6 in the tens place
  • Carry over 1 to the hundreds place (since 16 = 10 + 6)

3. Adding the Hundreds Place (2 + 3 + Carry)

• Calculation: 2 + 3 + 1 (carried) = 6
• Action:
  • Write 6 in the hundreds place

Final Answer: 665

Alternative Method: Expanded Form Addition

Breaking numbers into their place values:

276 = 200 + 70 + 6
389 = 300 + 80 + 9

Now add:

• Hundreds: 200 + 300 = 500
• Tens: 70 + 80 = 150
• Ones: 6 + 9 = 15

Combine all partial sums:
500 + 150 + 15 = 665

Practice Exercises:

Exercise 1: 34 + 59

1. Write vertically
2. Add ones place:
   4 (from 34) + 9 (from 59) = 13
   Write 3 in the ones place
   Carry over 1 to the tens place
3. Add tens place (with carry):
   3 (from 34) + 5 (from 59) + 1 (carried) = 9
4. Final answer:93
   Verification:
   30 + 50 = 80
   4 + 9 = 13
   80 + 13 = 93 ✓

Exercise 2: 25 + 46

1. Write vertically
2. Add ones place:
   5 + 6 = 11
   Write 1 in the ones place
   Carry over 1 to the tens place
3. Add tens place (with carry):
   2 + 4 + 1 (carried) = 7
4. Final answer: 71
   Alternative Method (Breaking Numbers):
   25 + 46 = (20 + 40) + (5 + 6) = 60 + 11 = 71 ✓

Exercise 3: 19 + 79

1. Write vertically
2. Add ones place:
   9 + 9 = 18
   Write 8 in the ones place
   Carry over 1 to the tens place
3. Add tens place (with carry):
   1 + 7 + 1 (carried) = 9
4. Final answer: 98

Exercise 4: 135 + 188

1. Write vertically (align by place value)
2. Add the ones place:
   5 (from 135) + 8 (from 188) = 13
   Write 3 in the ones place
   Carry over 1 to the tens place
3. Add the tens place (including carry):
   3 (from 135) + 8 (from 188) + 1 (carried) = 12
   Write 2 in the tens place
   Carry over 1 to the hundreds place
4. Add the hundreds place (including carry):
   1 (from 135) + 1 (from 188) + 1 (carried) = 3
   Write 3 in the hundreds place
   Verification:
   Break into parts:
   100 + 100 = 200
   30 + 80 = 110
   5 + 8 = 13
   Total: 200 + 110 + 13 = 323 ✓

Exercise 5: 147 + 234

1. Write the vertical setup
2. Add ones place:
   7 + 4 = 11
   Write 1 in ones place
   Carry 1 to tens
3. Add tens place:
   4 + 3 + 1 (carried) = 8
   Write 8 in tens place
4. Add hundreds place:
   1 + 2 = 3
   Write 3 in hundreds place
   Alternative Method (Expanded Form):
   147 = 100 + 40 + 7
   234 = 200 + 30 + 4
   Sum = 300 + 70 + 11 = 381 ✓

Exercise 5: 389 + 255

1. Write the vertical setup
2. Add ones place:
   9 + 5 = 14
   Write 4 in ones place
   Carry 1 to tens
3. Add tens place:
   8 + 5 + 1 (carried) = 14
   Write 4 in tens place
   Carry 1 to hundreds
4. Add hundreds place:
   3 + 2 + 1 (carried) = 6
   Write 6 in hundreds place

Final answer: 644