Addition Problem: Calculate 6324 + 2798 Using Column Method

Column Addition with Carrying Operations

6324+2798776 \begin{aligned} &6324 \\ +& \\ &2798\\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem together.
00:09 We'll combine the digits in pairs. Ready? Let's go.
00:14 First, add the ones. Ones with ones.
00:17 Place the result in the ones place. And carry one over to the tens.
00:23 Next, add the tens. Don't forget to add the one you carried.
00:28 Place it in the tens spot and carry one over to the hundreds.
00:32 Now, let's add the hundreds, plus the carried one.
00:36 Put that in the hundreds place and carry one to the thousands.
00:41 Finally, add the thousands, and don't forget the carried one.
00:46 Place it in the thousands.
00:49 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

6324+2798776 \begin{aligned} &6324 \\ +& \\ &2798\\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Set up the numbers for vertical addition:

6324+2798776 \begin{aligned} &6324 \\ +&2798\\ \underline{\phantom{776}} & \\ \end{aligned}

  • Step 2: Add the digits in the units place: 4+8=124 + 8 = 12, write down 22, carry over 11.

13  232 \begin{aligned} &\phantom{1} \\ &\phantom{3} \;232 \\ \end{aligned}

  • Step 3: Add the digits in the tens place: 2+9=112 + 9 = 11 plus carry 11 makes 1212. Write down 22, carry over 11.

13  32 \begin{aligned} &\phantom{1} \\ &\phantom{3} \;32 \\ \end{aligned}

  • Step 4: Add the digits in the hundreds place: 3+7=103 + 7 = 10 plus carry 11 makes 1111. Write down 11, carry over 11.

12  1 \begin{aligned} &\phantom{1} \\ &\phantom{2} \;1 \\ \end{aligned}

  • Step 5: Add the digits in the thousands place: 6+2=86 + 2 = 8 plus carry 11 makes 99. Write down 99.

97122 \begin{aligned} &\phantom{9}7122 \\ \end{aligned}

Therefore, the sum of 63246324 and 27982798 is 9122\mathbf{9122}.

3

Final Answer

9122

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up digits by place value columns correctly
  • Technique: Start from ones place: 4 + 8 = 12, write 2, carry 1
  • Check: Verify each column sum including carries: 6324 + 2798 = 9122 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry or adding carry digits incorrectly
    Don't ignore the carry digit from 4 + 8 = 12 when adding tens place = wrong final answer like 9022! The carry represents the extra ten that must be added to the next column. Always write down the ones digit and carry the tens digit to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &90 \\ +& \\ &~~9\\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does 'carry' mean in addition?

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When two digits add up to 10 or more, you write the ones digit in your answer and carry the tens digit to the next column. For example: 4 + 8 = 12, so write 2 and carry 1.

Why do I start from the right side?

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You start from the ones place (rightmost column) because any carrying affects the next column to the left. Working left to right would mean redoing columns when carries happen!

What if I get confused with multiple carries?

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Write small carry numbers above each column as you work. This helps you remember what to add: original digits + any carry from the previous column.

How can I check if my addition is correct?

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Try adding the numbers in reverse order: 2798+63242798 + 6324. You should get the same answer! You can also use estimation: 6300 + 2800 ≈ 9100.

What happens if there's a carry in the leftmost column?

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If the leftmost column creates a carry (like 6 + 2 + 1 = 9 here), just write it as part of your final answer. Sometimes this creates an extra digit in your sum!

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