Solve Three-Digit Addition: 281 + 507 in Vertical Format

Vertical Addition with Three-Digit Numbers

281+507776 \begin{aligned} &281 \\ +& \\ &507 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time we'll calculate the sum of 2 digits, and then substitute
00:06 Let's start by adding ones with ones, and substitute in ones
00:09 Add tens with tens, substitute in tens
00:14 Add hundreds with hundreds, substitute in hundreds
00:17 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

281+507776 \begin{aligned} &281 \\ +& \\ &507 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll perform vertical addition as follows:

  • Step 1: Align the numbers by columns (units, tens, hundreds).
    281+507 \begin{aligned} &281 \\ +& \\ &507 \\ \hline \end{aligned}

  • Step 2: Add the digits from the rightmost column to the leftmost:
    - Units place: Add 1 and 7, which equals 8. No carry is needed here.
    - Tens place: Add 8 and 0, which equals 8. No carry is needed here.
    - Hundreds place: Add 2 and 5, which equals 7. No carry is needed here.

Therefore, the sum of 281281 and 507507 is 788788.

The solution to the problem is 788 788 .

3

Final Answer

788

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value columns before adding
  • Technique: Add column by column from right to left: 1+7=8, 8+0=8, 2+5=7
  • Check: Verify by adding horizontally: 281+507=788 matches vertical result ✓

Common Mistakes

Avoid these frequent errors
  • Misaligning digits in wrong place value columns
    Don't line up numbers by their first digits instead of place values = completely wrong sum! This puts hundreds in tens place and creates massive errors. Always align by place value columns (ones under ones, tens under tens).

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

Why do I start adding from the right side?

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We start from the ones place (rightmost column) because if there's any carrying needed, it moves left to the next higher place value. This prevents confusion and ensures accuracy!

What if I need to carry when adding?

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When a column sum exceeds 9, write the ones digit below and carry the tens digit to the next left column. For example: 7+8=15, so write 5 and carry the 1.

How do I know my digits are lined up correctly?

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Make sure each column has the same place value: ones under ones, tens under tens, hundreds under hundreds. The rightmost digits should always be aligned vertically.

Can I add the numbers in a different order?

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Yes! Addition is commutative, so 281+507281 + 507 gives the same result as 507+281507 + 281. The vertical format just makes it easier to organize.

What if one number has fewer digits?

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Treat missing digits as zeros. For example, if adding 281 + 57, think of it as 281 + 057 to maintain proper alignment in all columns.

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