Calculate the Sum: 1054 + 353 in Vertical Format

Addition with Carrying Across Columns

1054+  353776 \begin{aligned} &1054 \\ +& \\ &~~353 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem together.
00:07 First, combine two digits at a time. Here's how.
00:12 We'll start by adding the ones digits.
00:16 Write down the result in the ones place.
00:19 Next, add the tens digits together.
00:23 Place the result in the tens spot, and carry one to the hundreds.
00:27 Now, let's add the hundreds digits. Don't forget to add the carried one.
00:32 Write the answer in the hundreds place.
00:36 Fill in any missing digits with zeros.
00:39 Finally, add the thousands digits and write the sum in the thousands place.
00:44 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1054+  353776 \begin{aligned} &1054 \\ +& \\ &~~353 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we will perform the vertical addition of 1054 and 353 as follows:

  • Step 1: Align the numbers:
      1054+ 35377600 \begin{array}{c} ~~ 1054 \\ + \ 353 \\ \underline{\phantom{77600}}\\ \end{array}

  • Step 2: Add the digits in the units place: 4+3=7 4 + 3 = 7 (no carry is needed).

  • Step 3: Add the digits in the tens place: 5+5=10 5 + 5 = 10 . Write down 0 and carry over 1 to the hundreds place.

  • Step 4: Add the digits in the hundreds place, including the carry: 0+3+1=4 0 + 3 + 1 = 4 (from the carry operation).

  • Step 5: Add the digits in the thousands place: 1+0=1 1 + 0 = 1 .

Thus, the solution is 1407 1407 .

Given the choices, the correct answer is choice 4:

1407

3

Final Answer

1407

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up numbers by place value columns correctly
  • Technique: Add column by column: 4+3=7, 5+5=10 (carry the 1)
  • Check: Verify by adding backwards: 1407 = 1000+400+0+7 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write 10 in the tens place when 5+5=10 = wrong answer 1517! The 10 means write 0 and carry 1 to the next column. Always carry any digit over 9 to the left 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 it mean to 'carry' in addition?

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When adding two digits gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example: 5+5=10, so write 0 and carry 1.

Why do I need to align the numbers vertically?

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Place value matters! The ones must line up with ones, tens with tens, etc. If numbers aren't aligned, you'll add the wrong digits together and get an incorrect answer.

What if I forget to carry a number?

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You'll get the wrong answer! Always check each column - if the sum is 10 or greater, you must carry. Practice writing small numbers above columns to remember your carries.

How can I check if my addition is correct?

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Try these methods:

  • Add the numbers in reverse order (353 + 1054)
  • Use estimation: 1054 + 353 ≈ 1000 + 350 = 1350, close to 1407 ✓
  • Subtract your answer minus one addend to get the other

Why is my answer different from the choices given?

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Double-check your carrying! The most common error is forgetting to add carried digits or writing them in the wrong place. Go through each column carefully, step by step.

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