Solve Vertical Addition: 683 + 127 Step-by-Step

Q: Why do we start adding from the right side instead of the left?

We start from the ones place (rightmost) because carrying moves left! If we started left, we'd have to go back and change our work when we carry. Starting right ensures we handle all carrying as we go.

Q: What if I forget to carry a number?

Your final answer will be too small! For example, if you forget to carry the 1 from $ 3 + 7 = 10 $, you might get 800 instead of 810. Always double-check your carrying.

Q: Can I add the numbers horizontally instead?

Yes, but vertical addition is more organized and reduces errors! It keeps place values aligned and makes carrying easier to track. Horizontal addition works for small numbers but gets confusing with larger ones.

Q: How do I know if I carried correctly?

Check each column: if the sum is 10 or more, you must carry. Write the ones digit below and carry the tens digit left. For $ 8 + 2 + 1 = 11 $, write 1 and carry 1.

Vertical Addition with Carrying Across Columns

$\begin{aligned} &683\\ +& \\ &127 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 Each time, we'll calculate the sum of two digits and substitute it.

00:12 Let's begin by adding the ones with the ones.

00:16 Place the sum in the ones position and add one to the tens.

00:21 Now, add the tens with the tens. Don't forget to include that one.

00:26 Put the sum in the tens place and add one to the hundreds.

00:30 Finally, add the hundreds with the hundreds. Include that extra one again.

00:36 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &683\\ +& \\ &127 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will use the vertical addition method:

Step 1: Align both numbers by their rightmost digits. This means: $683$ on top, $127$ on the bottom.
Step 2: Start adding from the rightmost column (the units place): $3 + 7 = 10$ . Write down $0$ and carry over $1$ to the tens column.
Step 3: Next, move to the tens place: $8 + 2 = 10$ ; add the carried over $1$ : $10 + 1 = 11$ . Write down $1$ and carry over $1$ to the hundreds column.
Step 4: Finally, move to the hundreds place: $6 + 1 = 7$ ; add the carried over $1$ : $7 + 1 = 8$ . Write down $8$ .

The sum of $683$ and $127$ is $810$ .

Therefore, the correct answer is $810$ .

Final Answer

810

Key Points to Remember

Essential concepts to master this topic

Rule: Always add from right to left, column by column
Technique: When sum exceeds 9, write ones digit and carry tens: $3 + 7 = 10$ → write 0, carry 1
Check: Verify by adding left to right: $600 + 80 + 3 + 100 + 20 + 7 = 810$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add the carried number to the next column
Don't just carry the 1 and forget to add it = wrong answer like 800 instead of 810! Students often remember to carry but forget the crucial step of adding it to the next column's sum. Always add the carried digit to your column sum before writing the result.

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 we start adding from the right side instead of the left?

We start from the ones place (rightmost) because carrying moves left! If we started left, we'd have to go back and change our work when we carry. Starting right ensures we handle all carrying as we go.

What if I forget to carry a number?

Your final answer will be too small! For example, if you forget to carry the 1 from $3 + 7 = 10$ , you might get 800 instead of 810. Always double-check your carrying.

Can I add the numbers horizontally instead?

Yes, but vertical addition is more organized and reduces errors! It keeps place values aligned and makes carrying easier to track. Horizontal addition works for small numbers but gets confusing with larger ones.

How do I know if I carried correctly?

Check each column: if the sum is 10 or more, you must carry. Write the ones digit below and carry the tens digit left. For $8 + 2 + 1 = 11$ , write 1 and carry 1.

What if there are more than two numbers to add?

The same rules apply! Add all digits in each column, carry when needed. With practice, you can add multiple numbers just as easily as two numbers.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime