Calculate the Sum: 7831 + 673 in Vertical Format

Vertical Addition with Multi-Digit Carrying

7831+  673776 \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's get started by solving the problem.
00:09 Each time, combine two digits carefully, like a puzzle.
00:13 Start by adding the ones digits together.
00:17 Then, place the result in the ones column.
00:20 Next, add the tens digits.
00:23 Place the result in the tens column. Don't forget to add 1 to the hundreds!
00:28 Now, add the hundreds digits. Include that extra 1.
00:33 Put the result in the hundreds column and add 1 to the thousands.
00:38 Place a zero in any missing spots.
00:41 Add the thousands digits, and remember the extra 1.
00:46 Place the final number in the thousands column.
00:49 And that's how we solve it! Great work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7831+  673776 \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the numbers by their place values:
  • 7831+  673776 \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ \end{aligned}

  • Step 2: Add the digits in each column, starting from the right (units) column.
  • The unit's column: 1+3=41 + 3 = 4. Write 4 under the units column.

  • Step 3: Move to the ten's column.
  • Add: 3+7=103 + 7 = 10. Write 0 under the tens and carry 1 to the hundreds column.

  • Step 4: Move to the hundred's column.
  • Add: 8+6=148 + 6 = 14, and don't forget the carried 1, making it 1515.

    Write 5 under the hundreds and carry 1 to the thousands.

  • Step 5: Move to the thousand's column.
  • Add: 7+1=87 + 1 = 8. Don't forget the carried 1, making it 88.

    Write 8 under the thousands.

    The sum of the numbers is:

    7831+  6737768504 \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ &8504 \\ \end{aligned}

Therefore, the sum of 7831 and 673 is 8504 \mathbf{8504} .

This corresponds to the choice: :

8504

.

3

Final Answer

8504

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place values before starting addition
  • Carrying: When column sum ≥ 10, write ones digit and carry tens to next column
  • Verification: Add column by column from right to left, checking each carry ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add carried values
    Don't ignore the carried 1 when moving to the next column = wrong final answer! In this problem, forgetting to add the carried 1 in the hundreds column gives 8404 instead of 8504. Always add the carried value to your column sum before writing the result.

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

Why do we start adding from the right side?

+

We start from the ones place because carrying moves from right to left! Just like when counting money - you handle pennies before dimes, dimes before dollars.

What if I forget to carry a number?

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Your final answer will be too small! In 7831 + 673, forgetting to carry the 1 from tens to hundreds gives you 8404 instead of the correct 8504.

How do I keep track of what I'm carrying?

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Write small numbers above the next column to remember your carries. For example, write a small '1' above the hundreds place when you carry from tens.

Can I add from left to right instead?

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It's much harder! Adding left to right means you might need to borrow or adjust later. The right-to-left method handles all carrying as you go.

What if both numbers don't have the same number of digits?

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Just imagine leading zeros! For 673, think of it as 0673 when adding to 7831. This keeps everything aligned properly.

How can I check if my answer is right?

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Try adding the numbers in reverse order: 673+7831 673 + 7831 . You should get the same answer, or use estimation: 7800 + 700 ≈ 8500 ✓

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