Calculate the Sum: 36715 + 45192 in Vertical Format

Multi-Digit Addition with Carrying Process

36715+45192776 \begin{aligned} &36715\\ +& \\ &45192 \\ &\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 place
00:06 Let's start by combining ones with ones
00:09 Place the ones
00:12 Combine tens with tens
00:15 Place tens in tens, and add 1 to hundreds
00:20 Combine hundreds with hundreds, remember to add 1 to the calculation
00:24 Place in hundreds
00:27 Combine thousands with thousands
00:31 Place in thousands, add 1 to tens of thousands
00:36 Combine tens of thousands with tens of thousands, add 1 to the calculation
00:42 Place in tens of thousands
00:45 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

36715+45192776 \begin{aligned} &36715\\ +& \\ &45192 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve the problem effectively, we will follow a systematic approach:

  • Step 1: Write the two numbers one above the other, aligning by columns according to their place value.
  • Step 2: Begin adding from the rightmost column (the units place), moving leftward. Remember to carry over any tens to the next place value.
  • Step 3: Continue to add column by column, including any carries from the previous column.

Let's work through these steps with the given numbers:

+36715+45192 \begin{aligned} &\phantom{+}36715 \\ + &45192 \\ \hline \end{aligned}

Units Column (far right):
5 (from 36715) + 2 (from 45192) = 7

Tens Column:
1 (from 36715) + 9 (from 45192) = 10
Write down 0, and carry over 1.

Hundreds Column:
7 (from 36715) + 1 (carry) + 1 (from 45192) = 9

Thousands Column:
6 (from 36715) + 5 (from 45192) = 11
Write down 1, and carry over 1.

Tens of Thousands Column:
3 (from 36715) + 4 (from 45192) + 1 (carry) = 8

Thus, the sum is:

+36715+4519281907 \begin{aligned} &\phantom{+}36715 \\ + &45192 \\ \hline &81907 \\ \end{aligned}

Therefore, the solution to the problem is 81907 81907 .

3

Final Answer

81907

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value columns for accurate addition
  • Carrying: When sum exceeds 9, write units digit and carry tens
  • Verification: Add from left to right to double-check: 30000 + 6000 + 700 + 10 + 90 + 7 = 81907 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when column sum exceeds 9
    Don't write down 10 in the tens column when 1 + 9 = 10! This creates wrong place values and incorrect final answers. Always write the units digit (0) and carry the tens digit (1) to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does 'carrying' mean in addition?

+

When adding a column gives you 10 or more, you write down the units digit and carry the tens digit to the next column. For example: 7 + 5 = 12, so write 2 and carry 1.

Why do I need to align the numbers by columns?

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Proper alignment ensures you're adding like place values together - units with units, tens with tens, etc. Misalignment leads to completely wrong answers!

What if I forget to add a carry from the previous column?

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Your final answer will be wrong! Always double-check each column to make sure you've included any carry from the column to the right.

How can I check my addition is correct?

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Try these methods:

  • Add again from bottom to top instead of top to bottom
  • Estimate: 36715 + 45192 is about 37000 + 45000 = 82000
  • Subtract: 81907 - 45192 should equal 36715

What happens if there's a carry in the leftmost column?

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When the leftmost column produces a carry, it becomes a new leftmost digit in your answer. For example: 9999 + 1 = 10000 (the carry becomes the new ten-thousands place).

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