Solve Addition: 46891 + 27108 in Vertical Format

Q: What does 'carry over' mean in addition?

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 + 7 = 13 $, so write 3 and carry the 1.

Q: Why do I start adding from the right side?

We start from the ones place (rightmost) because any carrying affects the next column to the left. This ensures we handle all carries properly as we move through each place value.

Q: What if I forget to add a carried number?

Your final answer will be wrong by multiples of 10, 100, 1000, etc. Always double-check each column to make sure you've added any carried digits from the previous column.

Q: How can I check if my vertical addition is correct?

Try these methods:Reverse order: Add the second number firstEstimation: Round both numbers and see if your answer is closeDigital root: Add all digits repeatedly until you get a single digit

Q: What happens if both numbers have different amounts of digits?

Always align by place value, not by length! Put shorter numbers to the right, and imagine leading zeros on the left. For example: 46891 + 7108 becomes 46891 + 07108.

Q: Can I add the columns in any order I want?

No! You must add from right to left (ones, then tens, then hundreds, etc.) because carrying only works in this direction. Adding left to right will give you incorrect results.

Vertical Addition with Multi-Digit Carrying

$\begin{aligned} &46891\\ +& \\ &27108 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:10 First, combine two digits at a time.

00:14 Start with adding ones with ones.

00:17 Place the sum in the ones column.

00:20 Next, add tens with tens. Place the result in the tens column.

00:28 Now, add hundreds with hundreds. Place it in the hundreds column.

00:34 Add the thousands with thousands.

00:37 Place the thousands, and add one to the tens of thousands.

00:41 Finally, add tens of thousands with tens of thousands and place the result.

00:48 And that’s how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &46891\\ +& \\ &27108 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this addition problem, follow these steps:

We'll first perform vertical addition with the given numbers:

46891
+27108

Align the numbers vertically, ensuring each digit lines up with the same place value:

 $\begin{array}{c} & 4 & 6 & 8 & 9 & 1 \\ + & 2 & 7 & 1 & 0 & 8 \\ \hline \end{array}$

Now, we add each column from right to left:
1. Units place: $1 + 8 = 9$ . Write 9.
2. Tens place: $9 + 0 = 9$ . Write 9.
3. Hundreds place: $8 + 1 = 9$ . Write 9.
4. Thousands place: $6 + 7 = 13$ . Write 3 and carry over 1 to the ten-thousands place.
5. Ten-thousands place: $4 + 2 + 1 \text{ (carry over)} = 7$ . Write 7.

The result is formed as:

 $\begin{array}{c} & 7 & 3 & 9 & 9 & 9 \\ \end{array}$ 
\)

Thus, the solution to the problem is $73999$ .

Final Answer

73999

Key Points to Remember

Essential concepts to master this topic

Place Value Alignment: Line up digits by place value columns correctly
Carry Over Technique: When 6 + 7 = 13, write 3 and carry 1
Verification Check: Add numbers in different order: 27108 + 46891 should equal 73999 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write down two-digit sums like 13 in one column = wrong place values! This creates answers like 746999 instead of 73999. Always write the units digit and carry the tens digit 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 'carry over' mean in addition?

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: $6 + 7 = 13$ , so write 3 and carry the 1.

Why do I start adding from the right side?

We start from the ones place (rightmost) because any carrying affects the next column to the left. This ensures we handle all carries properly as we move through each place value.

What if I forget to add a carried number?

Your final answer will be wrong by multiples of 10, 100, 1000, etc. Always double-check each column to make sure you've added any carried digits from the previous column.

How can I check if my vertical addition is correct?

Try these methods:

Reverse order: Add the second number first
Estimation: Round both numbers and see if your answer is close
Digital root: Add all digits repeatedly until you get a single digit

What happens if both numbers have different amounts of digits?

Always align by place value, not by length! Put shorter numbers to the right, and imagine leading zeros on the left. For example: 46891 + 7108 becomes 46891 + 07108.

Can I add the columns in any order I want?

No! You must add from right to left (ones, then tens, then hundreds, etc.) because carrying only works in this direction. Adding left to right will give you incorrect results.

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