Solve Vertical Addition: 33 + 8 Step-by-Step

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

When two digits add up to 10 or more, you write the ones digit in your answer and 'carry' the tens digit to the next column. For example, $3 + 8 = 11$ means write 1 and carry 1.

Q: Why can't I just write 11 in the ones place?

Each column can only hold one digit! Writing 11 would mean you have 11 ones, but 10 ones actually equals 1 ten. That's why we carry the extra ten to the tens column.

Q: What if there's no tens digit in one of the numbers?

Treat missing digits as zero! In this problem, 8 has no tens digit, so we think of it as 08. Then add: $3 + 0 + 1\text{ (carry)} = 4$.

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

Try adding the numbers horizontally (left to right): $33 + 8 = 41$. If you get the same answer both ways, you're correct!

Q: Do I always start adding from the right side?

Yes, always! Start with the ones place (rightmost column) and work left. This ensures you handle any carrying correctly from smaller to larger place values.

Vertical Addition with Carry-Over

$\begin{aligned} &33 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 First, add the digits in the ones place.

00:10 Begin by adding the ones digits.

00:14 Place these ones, then add the tens digits.

00:18 Don't forget, one was carried over.

00:21 Put a zero where there's no digit.

00:24 Now, add the tens, and remember that extra one.

00:28 Place this in the tens column.

00:31 And there you have it, that's your solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &33 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers by their place value.
Step 2: Begin adding from the rightmost column (ones place).
Step 3: Carry over any value over 9 to the next left column.
Step 4: Continue with the next column (tens place), including any carried over value.

Now, let's perform the addition:

Vertical addition setup:
$\begin{aligned} &33 \\ + &~~8 \\ &\underline{\phantom{776}} \end{aligned}$

Step 1: Add the ones digits: $3 + 8 = 11$ . We write 1 in the ones place and carry over 1 to the tens place.

Step 2: Add the tens digits (3 from 33 and 0 from 8, since it has no tens digit), including any carry: $3 + 1 = 4$ .

This gives us:

$\begin{aligned} &33 \\ + &~~8 \\ &\underline{\phantom{776}} \\ &41 \end{aligned}$

Therefore, the solution to the problem is $\textbf{41}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up numbers by place value columns correctly
Technique: Add ones first: $3 + 8 = 11$ , write 1 carry 1
Check: Verify by adding horizontally: $33 + 8 = 41$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't just write 11 in the ones place = wrong answer like 311! When ones digits sum to 10 or more, you must write the ones digit and carry the tens digit to the next column. Always carry over values greater than 9 to the left 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 it mean to 'carry over' in addition?

When two digits add up to 10 or more, you write the ones digit in your answer and 'carry' the tens digit to the next column. For example, $3 + 8 = 11$ means write 1 and carry 1.

Why can't I just write 11 in the ones place?

Each column can only hold one digit! Writing 11 would mean you have 11 ones, but 10 ones actually equals 1 ten. That's why we carry the extra ten to the tens column.

What if there's no tens digit in one of the numbers?

Treat missing digits as zero! In this problem, 8 has no tens digit, so we think of it as 08. Then add: $3 + 0 + 1\text{ (carry)} = 4$ .

How do I check if my vertical addition is correct?

Try adding the numbers horizontally (left to right): $33 + 8 = 41$ . If you get the same answer both ways, you're correct!

Do I always start adding from the right side?

Yes, always! Start with the ones place (rightmost column) and work left. This ensures you handle any carrying correctly from smaller to larger place values.

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