Solve Vertical Addition: 845 + 27 Step by Step

Vertical Addition with Carrying Over

845+  27776 \begin{aligned} &845 \\ +& \\ &~~27 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 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, and add 1 to the tens
00:13 combine tens with tens, remember to add 1 to the calculation
00:17 place in the tens
00:20 place 0 in the missing digits
00:23 combine hundreds with hundreds, place in hundreds
00:26 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

845+  27776 \begin{aligned} &845 \\ +& \\ &~~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 vertically by place value.
  • Step 2: Start adding from the rightmost column (ones place), carrying over when necessary.
  • Step 3: Add all columns and account for any carried-over digits.

Now, let's work through each step:
Step 1: Align the numbers:
845+ 27\begin{aligned} &845 \\ + &~27 \\ \end{aligned}

Step 2: Add the digits in the ones place:
5+7=125 + 7 = 12. Write 2 below the line in the ones place, carry over 1 to the tens place.

Step 3: Add the digits in the tens place, including the carry:
4+2+1=74 + 2 + 1 = 7. Write 7 below the line in the tens place.

Step 4: Add the digits in the hundreds place:
Since there is no carry here, it's 8+0=88 + 0 = 8. Write 8 in the hundreds place.

Therefore, the sum is 872872, which corresponds to choice 1.

3

Final Answer

872

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value with ones digits aligned vertically
  • Technique: Start from ones place: 5 + 7 = 12, write 2 and carry 1
  • Check: Verify by adding horizontally: 845 + 27 = 872 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write 12 in the ones place when 5 + 7 = 12 = wrong alignment! This creates extra digits and makes the answer 10 times too large. Always carry the tens digit to the next column and write only the ones digit.

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 'carry over' mean in addition?

+

When two digits add up to 10 or more, you write down the ones digit and carry the tens digit to the next column. For example, 5 + 7 = 12, so write 2 and carry the 1.

Why do I need to align the numbers vertically?

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Aligning by place value ensures you're adding ones to ones, tens to tens, and hundreds to hundreds. Misalignment leads to completely wrong answers!

What if there's no digit in a place value?

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Treat it as zero! In this problem, 27 has no hundreds digit, so it's really 027. Add 8 + 0 = 8 in the hundreds place.

How do I know when to carry over?

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Carry over whenever the sum of digits in any column is 10 or greater. The tens part goes to the next column, and the ones part stays in the current column.

Can I add from left to right instead?

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It's possible but much harder! Adding from right to left (ones to hundreds) makes carrying over easier to track and prevents mistakes.

What if I need to carry over multiple times?

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That's normal! Just handle one column at a time, carrying over as needed. Remember to add any carried digit when working on each new column.

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