Solve Vertical Addition: 367 + 41 Step-by-Step

Vertical Addition with Carrying

367+  41776 \begin{aligned} &367 \\ +& \\ &~~41 \\ &\underline{\phantom{776}} & \\ \end{aligned}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time we calculate addition of 2 digits, and then we substitute
00:06 Let's start by adding ones with ones
00:09 We substitute the ones
00:12 We add tens with tens
00:15 We substitute tens in tens place, add 1 to hundreds
00:19 We put 0 in the missing digits
00:22 We add hundreds with hundreds remember to add 1, substitute in hundreds
00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

367+  41776 \begin{aligned} &367 \\ +& \\ &~~41 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we will perform the vertical addition of the numbers 367 and 41:

  • Step 1: Write the numbers vertically and align them by their place values as follows: 367+  41 \begin{aligned} & 367 \\ + & \underline{~~41} \\ \end{aligned}
  • Step 2: Start by adding the digits in the units column:
    The units column: 7+1=87 + 1 = 8.
    Write 8 in the units place of the result.
  • Step 3: Move to the tens column:
    The tens column: 6+4=106 + 4 = 10.
    Since the sum is 10, write 0 in the tens place and carry over the 1 to the hundreds column.
  • Step 4: Finally, add the digits in the hundreds column with the carryover:
    The hundreds column: 3+1=43 + 1 = 4.
    Write 4 in the hundreds place. (There is no carryover here, as all is included.)
  • Step 5: Combine the digits to form the final sum.
    The result after summing is 408.

Therefore, the solution to the sum of 367 and 41 is 408408.

3

Final Answer

408

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value to ensure accurate addition
  • Technique: Add column by column: 7+1=87+1=8, 6+4=106+4=10, carry the 1
  • Check: Verify by adding left to right: 367 + 41 = 408 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when column sum exceeds 9
    Don't write 10 in the tens place when 6+4=10! This creates a two-digit number in a single column, making your answer completely wrong. Always carry the 1 to the next column and write only 0 in the current place.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does 'carrying' mean in addition?

+

When a column adds up to 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example, when 6+4=106+4=10, write 0 and carry 1.

Why do I need to align the numbers vertically?

+

Place value alignment is crucial! Units must line up with units, tens with tens, etc. Without proper alignment, you'll add wrong digits together and get an incorrect answer.

What if one number has fewer digits than the other?

+

That's normal! In 367 + 41, there's no hundreds digit for 41, so treat it as 0. You're really adding 367 + 041, making the hundreds column 3 + 0 = 3.

How can I check my vertical addition answer?

+

Try these methods:

  • Add the numbers horizontally instead: 367 + 41
  • Reverse the order: 41 + 367 should give the same answer
  • Use estimation: 367 ≈ 370, so 370 + 41 = 411 (close to 408)

What happens if I need to carry multiple times?

+

No problem! Handle each carry one column at a time. If you have 367 + 285, you might carry from units to tens, then from tens to hundreds. Just work systematically from right to left.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations