Solve Vertical Addition: 631 + 9 Step by Step

Q: Why do I need to line up the numbers by place value?

Place value alignment ensures you're adding ones to ones, tens to tens, and hundreds to hundreds. Without proper alignment, you'll get completely wrong answers!

Q: What does 'carry' mean in addition?

When digits add up to 10 or more, you write the ones digit and carry the tens digit to the next column. Think of it as moving the extra ten to where it belongs!

Q: How do I know when to carry?

Carry whenever the sum in any column is 10 or greater. For example, 1 + 9 = 10, so write 0 and carry 1 to the tens place.

Q: What if there's nothing in a column to add?

If one number has fewer digits, treat the empty spaces as zeros. In 631 + 9, the tens place becomes 3 + 0 = 3 (plus any carry-over).

Q: Can I add from left to right instead?

It's much easier to add from right to left because carrying flows naturally to the left. Adding left to right makes carrying complicated and error-prone.

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

Use reverse addition: subtract one addend from your answer. If you get the other addend, you're correct! Example: 640 - 9 = 631 ✓

Vertical Addition with Single-Digit Carrying

$\begin{aligned} &631 \\ +& \\ &~~~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time consider combining 2 digits, and then place

00:06 Let's start by combining ones with ones

00:09 Place the ones in ones, add 1 to tens

00:12 Place 0 in the missing digits

00:16 Combine the tens, remember to add 1, and place in tens

00:19 Place 0 in the missing digits

00:23 Combine the hundreds, and place in hundreds

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &631 \\ +& \\ &~~~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll perform vertical addition for the numbers 631 and 9, handling any necessary carrying.

Align the numbers based on their place value:

$\begin{aligned} &631 \\ +& \\ &~~~9 \\ \end{aligned}$

Step 1: Add the units place (rightmost column).
- We have 1 (from 631) + 9 = 10.
- Write 0 and carry over 1 to the tens place.
Step 2: Add the tens place (second column from the right).
- We have 3 (from 31) + 0 + 1 (carry-over) = 4.
- Write 4 in the tens place.
Step 3: Add the hundreds place (leftmost column).
- We have 6 only (as there’s nothing else to add).
- Write 6 in the hundreds place.

Thus, the final sum of 631 and 9 is 640.

Therefore, the solution to the problem is $\textbf{640}$ .

Final Answer

640

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Line up digits by place value before adding
Carrying Technique: When 1 + 9 = 10, write 0 and carry 1
Verification: Check that 631 + 9 equals your answer: 640 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry when sum exceeds 9
Don't write 19 in the ones place when 1 + 9 = 10! This creates invalid multi-digit place values and wrong answers. Always carry the tens digit to the next column and write only the ones digit.

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 line up the numbers by place value?

Place value alignment ensures you're adding ones to ones, tens to tens, and hundreds to hundreds. Without proper alignment, you'll get completely wrong answers!

What does 'carry' mean in addition?

When digits add up to 10 or more, you write the ones digit and carry the tens digit to the next column. Think of it as moving the extra ten to where it belongs!

How do I know when to carry?

Carry whenever the sum in any column is 10 or greater. For example, 1 + 9 = 10, so write 0 and carry 1 to the tens place.

What if there's nothing in a column to add?

If one number has fewer digits, treat the empty spaces as zeros. In 631 + 9, the tens place becomes 3 + 0 = 3 (plus any carry-over).

Can I add from left to right instead?

It's much easier to add from right to left because carrying flows naturally to the left. Adding left to right makes carrying complicated and error-prone.

How can I check if my answer is correct?

Use reverse addition: subtract one addend from your answer. If you get the other addend, you're correct! Example: 640 - 9 = 631 ✓

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