Solve the Addition Problem: Calculate 52 + 9 in Vertical Format

Q: Why do I need to carry over the 1 when I get 11?

Because each place value can only hold one digit! When 2 + 9 = 11, you write the 1 in the ones place and carry the other 1 to the tens place. This keeps your answer in proper place value form.

Q: Can I add from left to right instead?

It's better to add from right to left (ones first, then tens). This way, you handle any carrying as you go, making it less likely to make mistakes.

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

Try adding the numbers horizontally to double-check! $ 52 + 9 = 61 $ should give you the same answer as your vertical method.

Vertical Addition with Two-Digit Regrouping

$\begin{aligned} &52 \\ +& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's solve this math problem together.

00:06 First, calculate the sum of two digits.

00:09 Start by adding the ones digits together.

00:13 Write down the ones digit and add tens to tens.

00:17 Don't forget to carry over one if needed.

00:20 Use zero if there is no digit to add.

00:23 Now, add the tens digits. Remember to add one if carried.

00:29 Place the result in the tens column.

00:32 And that's how you get the answer to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &52 \\ +& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will use vertical addition to find the sum of 52 and 9. Let's follow the steps outlined:

Step 1: Align the numbers.
Write the numbers so that the ones digits align vertically:

$\begin{array}{cc} & 5 & 2 \\ + & & 9 \\ \hline \end{array}$

Step 2: Add the ones digits.
First, add the digits in the far right column (ones place): $2 + 9 = 11$ .
Step 3: Handle the carry-over.
Since 11 is greater than 9, write the 1 in the ones place and carry over the 1 to the tens place:

$\text{Carry: } 1 \quad \quad$ $\begin{array}{cc} & 5 & 2 \\ + & & 9 \\ \hline & 6 & 1 \\ \end{array}$

Step 4: Add the tens digits, including any carry-over.
Next, add the digits in the tens place: $5 + 1 = 6$ .
Step 5: Write the final result.

Therefore, the sum of 52 and 9 is $61$ .

The correct answer is choice $3$ with the final total being $61$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers with ones and tens digits properly aligned
Regrouping: When sum exceeds 9, write ones digit and carry tens
Verification: Check by adding horizontally: 52 + 9 = 50 + 11 = 61 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 11 in the ones place = wrong answer like 511! When ones digits sum to more than 9, you must write only the ones digit and carry the tens digit to the next column. Always carry over when the sum is 10 or greater.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

Why do I need to carry over the 1 when I get 11?

Because each place value can only hold one digit! When 2 + 9 = 11, you write the 1 in the ones place and carry the other 1 to the tens place. This keeps your answer in proper place value form.

What if I forget to add the carried number?

You'll get the wrong answer! In this problem, forgetting to add the carried 1 would give you 51 instead of 61. Always remember to add any carried digits to the next column.

Can I add from left to right instead?

It's better to add from right to left (ones first, then tens). This way, you handle any carrying as you go, making it less likely to make mistakes.

How do I know if my vertical addition is correct?

Try adding the numbers horizontally to double-check! $52 + 9 = 61$ should give you the same answer as your vertical method.

What if both numbers have different amounts of digits?

No problem! Just align them by place value. The number 9 is the same as 09, so it lines up under the 2 in 52. The empty space above the 9 in the tens column means there's a 0 there.

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