Solve Vertical Addition: 352 + 27 Step-by-Step

Vertical Addition with Two-Digit Numbers

352+  27776 \begin{aligned} &352 \\ +& \\ &~~27 \\ &\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 solve this problem together!
00:08 We'll add two digits at a time. Ready?
00:12 First, let's add the ones place. Put the answer with the ones.
00:17 Next, add the tens place. Place the sum in the tens spot.
00:22 If any digits are missing, just place a zero there.
00:26 Now, add the hundreds place, and put it with the hundreds.
00:30 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

352+  27776 \begin{aligned} &352 \\ +& \\ &~~27 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Align the numbers based on place value.
  • Step 2: Add each column starting from the right (units column).
  • Step 3: Carry over any values greater than 9 to the next column.

Now, let’s work through each step:

Step 1: Align the numbers vertically:

352+27 \begin{array}{c} 352 \\ + 27 \\ \hline \end{array}

Step 2: Add the right-most column (the units).
2+7=92 + 7 = 9, write 99 in the units place.

Step 3: Move to the next column to the left (the tens).
5+2=75 + 2 = 7, write 77 in the tens place (no carrying needed).

Step 4: Move to the left-most column (the hundreds).
33 remains 33 as there is nothing to add, so write 33 in the hundreds place.

Thus, the result when you add the numbers is:

352+27379 \begin{array}{c} 352 \\ + 27 \\ \hline 379 \\ \end{array}

Therefore, the sum of 352352 and 2727 is 379379.

3

Final Answer

379

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value with units under units
  • Technique: Add from right to left: 2+7=9, then 5+2=7
  • Check: Verify each column adds correctly: 379 has correct digits ✓

Common Mistakes

Avoid these frequent errors
  • Misaligning numbers by digits instead of place value
    Don't line up 352 and 27 by total digits = wrong column additions! This puts tens under units and creates calculation errors. Always align numbers by place value with rightmost digits lined up.

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 need to line up the numbers in columns?

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Place value alignment is crucial! Each column represents a different place value (units, tens, hundreds). When numbers aren't aligned properly, you're adding the wrong digits together.

What if one number has fewer digits than the other?

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That's normal! In this problem, 27 has no hundreds digit, so we treat it as having 0 in the hundreds place. Just make sure the rightmost digits line up in the units column.

Do I always start adding from the right side?

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Yes! Always start from the rightmost column (units place) and work left. This ensures you handle any carrying correctly when sums exceed 9.

What happens if a column adds up to more than 9?

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You'll need to carry over! Write down the units digit and carry the tens digit to the next column. In this problem, no carrying was needed since all column sums were less than 10.

How can I check if my answer is right?

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Try reverse checking: subtract one of the original numbers from your answer. 37927=352379 - 27 = 352 ✓ This confirms your addition is correct!

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