Calculate the Sum: 228 + 512 in Vertical Format

Addition with Carrying and Place Value

228+512776 \begin{aligned} &228 \\ +& \\ &512 \\ &\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 calculate the sum of 2 digits, and then substitute
00:06 Let's start by adding ones with ones
00:09 Place the ones, add 1 to the tens
00:14 Add tens with tens, remember to add 1 to the calculation
00:18 Place in tens
00:25 Add hundreds with hundreds, place in hundreds
00:28 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

228+512776 \begin{aligned} &228 \\ +& \\ &512 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll perform the vertical addition of the given numbers:

  • Step 1: Write the numbers 228228 and 512512 vertically aligned by place value:

228+512 \begin{array}{c} \\ &228 \\ + &512 \\ \hline \end{array}

  • Step 2: Add the digits in the ones column (8+28 + 2). This sum is 1010. Write down 00 in the ones place and carry over 11 to the tens column.

1228+512?0 \begin{array}{c} 1 \\ &228 \\ +&512 \\ \hline & ?0 \\ \end{array}

  • Step 3: Add the digits in the tens column (2+12 + 1) along with the carry of 11. This gives 44. Write 44 in the tens place.

228+512?40 \begin{array}{c} &228 \\ +&512 \\ \hline & ?40 \\ \end{array}

  • Step 4: Add the digits in the hundreds column (2+52 + 5). This sum is 77. Write down 77 in the hundreds place.

228+512740 \begin{array}{c} &228 \\ +&512 \\ \hline &740 \\ \end{array}

Thus, the final answer is 740740.

Therefore, the solution to the problem is 740 740 .

3

Final Answer

740

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers with ones, tens, and hundreds columns perfectly aligned
  • Carrying: When sum exceeds 9, write remainder and carry 1 to next column
  • Verification: Check by adding in reverse order: 512 + 228 = 740 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry when column sum exceeds 9
    Don't write 10 in the ones place when 8 + 2 = 10! This ignores place value rules and gives wrong totals. Always write the ones digit (0) and carry the tens digit (1) to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does 'carrying' mean in addition?

+

When you add digits in a column and get 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example, 8+2=10 8 + 2 = 10 , so write 0 and carry 1.

Why do I need to align the numbers vertically?

+

Place value alignment is crucial! The ones digits must be under ones, tens under tens, etc. Misalignment leads to adding wrong place values and incorrect answers.

What if I forget to add the carried number?

+

You'll get the wrong answer! In this problem, forgetting the carried 1 in the tens column would give 2+1=3 2 + 1 = 3 instead of 2+1+1=4 2 + 1 + 1 = 4 , making your final answer 730 instead of 740.

How can I check if my addition is correct?

+

Try these methods:

  • Reverse addition: Add the numbers in opposite order
  • Estimation: Round to nearest hundreds: 200 + 500 = 700 (close to 740)
  • Subtraction check: 740 - 228 should equal 512

What if there are more than two numbers to add?

+

The same rules apply! Align all numbers by place value, add column by column from right to left, and carry when needed. Just take your time with each column.

🌟 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