Solve the Addition Problem: 977 + 23 in Vertical Format

Q: What does 'carry over' mean exactly?

When adding digits gives you 10 or more, you write down the units digit and carry the tens digit to the next column. For example: $7 + 3 = 10$, so write 0 and carry 1.

Q: Why do we add from right to left?

We start with the units place (ones) because any carryover affects the next column to the left. This ensures we handle all place values correctly from smallest to largest.

Q: What if I get multiple carryovers in a row?

That's normal! In this problem, we carried over three times: units to tens, tens to hundreds, and hundreds to thousands. Just handle each carryover one column at a time.

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

You can reverse-check by doing $1000 - 23 = 977$, or add the numbers horizontally: $900 + 70 + 7 + 20 + 3 = 1000$.

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

Always align by place value! Put units under units, tens under tens, etc. Empty places count as zero, so 23 is really 023 when aligned with 977.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this problem together!

00:06 First, think about combining two digits at a time.

00:10 Start by multiplying the ones digits first. Alright?

00:15 Place the result in the ones position, then carry over 1 to the tens.

00:20 Next, multiply the tens digits. Remember, add the carry over of 1.

00:25 Place your result in the tens position and carry over 1 to the hundreds.

00:30 Don’t forget to fill in any missing digits with zero.

00:34 Now, multiply the hundreds digits. Again, add 1 to the total.

00:39 Put this result in the hundreds place, and carry over 1 to the thousands.

00:44 Fill any remaining gaps with zero once more.

00:48 Finally, multiply the thousands digits and remember to add 1.

00:52 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

1

Understand the problem

$\begin{aligned} &977\\ +& \\ &~~23 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this vertical addition problem, we follow these steps:

Step 1: Align the numbers for vertical addition:
$\ \ \ 977$
$+ 23$
Step 2: Start by adding the units digits.
The units digit of $977$ is $7$ and the units digit of $23$ is $3$ .
$7 + 3 = 10$ . Write $0$ in the units place and carry over $1$ to the tens place.
Step 3: Add the tens digits including the carryover.
The tens digit of $977$ is $7$ and the tens digit of $23$ is $2$ .
Including the carryover $1$ :
$7 + 2 + 1 = 10$ . Write $0$ in the tens place and carry over $1$ to the hundreds place.
Step 4: Add the hundreds digits including the carryover.
The hundreds digit of $977$ is $9$ . There are no hundreds in $23$ , so only the carryover $1$ is added:
$9 + 1 = 10$ . Write $0$ in the hundreds place and carry over $1$ to the thousands place.
Step 5: Since $23$ does not have a thousands place digit, just write the $1$ from the previous carryover in the thousands place.

After completing all these steps, the final sum is $1000$ .

3

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers right-to-left by place value positions
Technique: Add column by column: $7 + 3 = 10$ , carry the 1
Check: Count total digits and verify: $977 + 23 = 1000$ has 4 digits ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 10 in a single column = wrong place values! When $7 + 3 = 10$ , this creates an invalid two-digit result in one place. Always write the units digit (0) 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 'carry over' mean exactly?

+

When adding digits gives you 10 or more, you write down the units digit and carry the tens digit to the next column. For example: $7 + 3 = 10$ , so write 0 and carry 1.

Why do we add from right to left?

+

We start with the units place (ones) because any carryover affects the next column to the left. This ensures we handle all place values correctly from smallest to largest.

What if I get multiple carryovers in a row?

+

That's normal! In this problem, we carried over three times: units to tens, tens to hundreds, and hundreds to thousands. Just handle each carryover one column at a time.

How can I check if my answer is right?

+

You can reverse-check by doing $1000 - 23 = 977$ , or add the numbers horizontally: $900 + 70 + 7 + 20 + 3 = 1000$ .

What if the numbers have different amounts of digits?

+

Always align by place value! Put units under units, tens under tens, etc. Empty places count as zero, so 23 is really 023 when aligned with 977.

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Solve the Addition Problem: 977 + 23 in Vertical Format

Vertical Addition with Multiple Carryovers

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