Solve Vertical Addition: 346 + 965 Step by Step

Vertical Addition with Three-Digit Carrying

346+965776 \begin{aligned} &346 \\ +& \\ &965 \\ &\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 consider combining 2 digits, and then we'll place
00:06 Let's start by combining ones with ones
00:09 Place the ones, add 1 to the tens
00:13 Combine tens with tens, remember to add 1 to the calculation
00:19 Place tens in tens, add 1 to hundreds
00:23 Combine hundreds with hundreds, remember to add 1
00:29 Place hundreds in hundreds, and add 1 to thousands
00:33 Place 0 in the missing digits
00:37 Combine thousands with thousands, remember to add 1
00:40 Place in thousands
00:43 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

346+965776 \begin{aligned} &346 \\ +& \\ &965 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Write the numbers 346 and 965 in a columnar fashion, aligning them by place value.
  • Step 2: Add the numbers starting with the ones place.
  • Step 3: Move to the tens place and add the digits, including any carry from the ones place.
  • Step 4: Continue to the hundreds place, again including any carry from the tens place.

Let's break this down:

Step 1: Write vertically:
346+965\begin{aligned} &346\\ + &965\\ \end{aligned}

Step 2: Add the ones place:
6+5=116 + 5 = 11. Write down 1 and carry over 1 to the tens place.

Step 3: Add the tens place (including carry):
4+6=104 + 6 = 10, plus the carry 1 makes 11. Write down 1 and carry over 1 to the hundreds place.

Step 4: Add the hundreds place (including carry):
3+9=123 + 9 = 12, plus the carry 1 makes 13. Write down 13 as there are no more places to carry over.

Thus, the sum of 346 and 965 is 1311\underline{1311}.

Therefore, the solution to the problem is 1311\mathbf{1311}.

3

Final Answer

1311

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Place digits in columns by ones, tens, hundreds positions
  • Technique: Add ones first: 6 + 5 = 11, write 1 carry 1
  • Check: Work backwards: 1311 - 965 = 346 confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write 11 in the ones place when 6 + 5 = 11 = wrong placement! This creates impossible multi-digit single positions. Always write the ones digit (1) and carry the tens digit (1) 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 'carrying over' mean exactly?

+

When adding digits gives you 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example, 6 + 5 = 11 means write 1 and carry 1.

Why do I start adding from the right side?

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We start from the ones place because any carrying affects the next column to the left. If we started from the left, we'd have to go back and fix our work when we carry!

What if I have to carry multiple times?

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That's normal! In this problem, we carry from ones to tens and from tens to hundreds. Just handle one column at a time and don't forget your carried numbers.

How can I check my addition without subtracting?

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Try adding in reverse order: 965 + 346. You should get the same answer (1311). You can also estimate: 300 + 900 ≈ 1200, so 1311 seems reasonable!

What if my final answer has more digits than either starting number?

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That's perfectly fine! When we carry from the hundreds place (3 + 9 + 1 = 13), we get a four-digit result. This happens when the sum is 1000 or greater.

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