Solve Multi-Digit Addition: 10256 + 17435 in Vertical Format

Q: What does 'carrying' mean in addition?

When adding a column 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, so write 1 and carry 1.

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

We start from the ones place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd miss these carried values!

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

Your answer will be wrong by that carried amount. In this problem, forgetting the carried 1 in the tens column would give 27681 instead of 27691. Always double-check your carries!

Q: How can I check if my answer is correct?

You can reverse-check by subtracting one addend from your sum. For example: $ 27691 - 10256 = 17435 $ ✓ This confirms our answer!

Q: What if the numbers have different amounts of digits?

No problem! Just imagine leading zeros for the shorter number. In this case, think of 10256 as having the same 5 digits as 17435, so they align properly.

Multi-Digit Addition with Carrying

$\begin{aligned} &10256\\ +& \\ &17435 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 write down

00:06 Let's start by combining ones with ones

00:09 Write down the ones, and add 1 to the tens

00:14 Combine tens with tens, remember to add 1 to the calculation

00:18 Write down in the tens place

00:24 Combine hundreds with hundreds, write down in hundreds place

00:29 Combine thousands with thousands, and write down in thousands place

00:35 Combine tens of thousands with tens of thousands, and write down

00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &10256\\ +& \\ &17435 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Start by adding the numbers column by column from right to left.
Step 2: Handle any carries appropriately as you move from one column to the next.
Step 3: Verify the result by comparing it to the provided answer choices.

Now, let's perform the addition step by step:

Step 1: Add the units column:
6 (from 10,256) + 5 (from 17,435) = 11
Write down 1 and carry over 1 to the tens column.

Step 2: Add the tens column:
5 + 3 = 8, plus the carry over 1, totals 9.
Write down 9.

Step 3: Add the hundreds column:
2 + 4 = 6.
Write down 6.

Step 4: Add the thousands column:
0 + 7 = 7.
Write down 7.

Step 5: Add the ten-thousands column:
1 + 1 = 2.
Write down 2.

Therefore, the sum of 10,256 and 17,435 is $27,691$ .

Final Answer

27691

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with rightmost digits aligned
Carrying: When sum exceeds 9, write ones digit and carry tens
Verification: Check each column addition: 6+5=11, write 1 carry 1 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't write 11 in the units place when 6+5=11! This creates an impossible two-digit number in a single column. Always write the ones digit (1) and carry the tens digit (1) to the next column.

Practice Quiz

Test your knowledge with interactive questions

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

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 ones digit and carry the tens digit to the next column. For example: 6+5=11, so write 1 and carry 1.

Why do I start adding from the right side?

We start from the ones place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd miss these carried values!

What if I forget to add a carried number?

Your answer will be wrong by that carried amount. In this problem, forgetting the carried 1 in the tens column would give 27681 instead of 27691. Always double-check your carries!

How can I check if my answer is correct?

You can reverse-check by subtracting one addend from your sum. For example: $27691 - 10256 = 17435$ ✓ This confirms our answer!

What if the numbers have different amounts of digits?

No problem! Just imagine leading zeros for the shorter number. In this case, think of 10256 as having the same 5 digits as 17435, so they align properly.

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