Solve Vertical Addition: 23 + 7 Step-by-Step

Q: Why do I need to carry the 1 when I get 10?

When you add digits and get a two-digit number, you can only write one digit in each place value column. The tens digit (1) must move to the tens column, and the ones digit (0) stays in the ones column.

Q: How do I know if I aligned the numbers correctly?

Line up the rightmost digits first! The ones place should be directly under the ones place. Count from right to left: ones, tens, hundreds.

Q: Can I add from left to right instead?

No! Always start from the rightmost column (ones place) and work left. This way, any carrying affects the next column properly. Left-to-right addition often leads to mistakes.

Vertical Addition with Carrying

$\begin{aligned} &23 \\ + \\ &~~7 \\ & \underline{\phantom{776}} \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve a math problem together.

00:07 Think about combining two digits at a time.

00:10 First, add the ones place. Ones with ones.

00:14 Great! Now place the ones and move on.

00:17 Remember, you might need to carry over one.

00:20 Put a zero where there's no digit.

00:24 Next, add your tens place. Don't forget to add the one you carried.

00:28 Place your solution in the tens place. You're almost there!

00:32 And there you have it. That's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &23 \\ + \\ &~~7 \\ & \underline{\phantom{776}} \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition as follows:

Step 1: Write the numbers in a column, aligning them by the right:
$\begin{array}{c} 23 \\ + 7 \\ \hline \end{array}$
Step 2: Add the digits in the rightmost column (ones place):
The digits are 3 and 7. So, $3 + 7 = 10$ . Write 0 in the ones place and carry over 1 to the tens place.
$\begin{array}{c} 23 \\ + 7 \\ \hline ~~~ 0 \end{array}$
Step 3: Add the digits in the tens place:
The digits are 2 and, due to the carry, 1. So, $2 + 1 = 3$ . Write 3 in the tens place.
$\begin{array}{c} 1~~ \\ 23 \\ + 7~ \\ \hline 30 \end{array}$

Therefore, the sum of 23 and 7 is $30$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value, rightmost digits together
Technique: Add ones first: 3 + 7 = 10, write 0 carry 1
Check: Count up from 23 by 7: 24, 25, 26, 27, 28, 29, 30 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry when sum exceeds 9
Don't just write 10 in the ones place when 3 + 7 = 10! This gives you 23 + 7 = 2310, which is completely wrong. Always write the ones digit (0) and carry the tens digit (1) to the next 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

Why do I need to carry the 1 when I get 10?

When you add digits and get a two-digit number, you can only write one digit in each place value column. The tens digit (1) must move to the tens column, and the ones digit (0) stays in the ones column.

What if I don't have a digit in the tens place for the second number?

That's fine! When adding 23 + 7, think of 7 as 07. The tens place of 7 has an invisible zero, so you're really adding $2 + 0 + 1$ (including the carry).

How do I know if I aligned the numbers correctly?

Line up the rightmost digits first! The ones place should be directly under the ones place. Count from right to left: ones, tens, hundreds.

Can I add from left to right instead?

No! Always start from the rightmost column (ones place) and work left. This way, any carrying affects the next column properly. Left-to-right addition often leads to mistakes.

What happens if both numbers in a column add to more than 10?

Same rule applies! For example, if you have 8 + 9 = 17, write 7 in that column and carry 1 to the next column to the left.

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