Solve Vertical Addition: 12 + 8 Step by Step

Q: Why do I need to line up the numbers vertically?

Aligning by place value ensures you're adding units to units and tens to tens! If numbers aren't lined up properly, you'll add the wrong digits together.

Q: What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and 'carry' the tens digit to the next column on the left. Think of it as borrowing in reverse!

Q: Do I always start from the right side?

Yes! Always start from the rightmost column (units place) and work left. This ensures you handle any carrying correctly as you move to bigger place values.

Q: What if there's no number in one column?

Treat empty spaces as zero. In this problem, there's no tens digit for 8, so we imagine it as 08, making the tens column 1 + 0 = 1 (plus our carried 1).

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

Use horizontal addition as a check: $ 12 + 8 = 20 $. You can also try adding in reverse: $ 8 + 12 = 20 $. Both should match your vertical result!

Vertical Addition with Carrying Technique

$\begin{aligned} &12 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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, add the tens to the tens

00:14 Remember 1 to carry over

00:17 Combine tens with tens, remember to add 1

00:21 Place 0 where there is no digit

00:27 Place the solution in tens

00:30 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

$\begin{aligned} &12 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To approach this problem, we'll use vertical addition of the numbers 12 and 8:

Step 1: Write the numbers vertically, aligning their place values.
$\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &~~? \\ \end{aligned}$
Step 2: Start adding from the rightmost column (units position).
Add the units: $2 + 8 = 10$ .
Write down the 0 in the units column and carry over the 1 to the tens column.
Step 3: Move to the next column on the left (tens position).
Add the tens: $1 + 1 = 2$ (including the carryover 1).
Write down the result in the tens column.
Step 4: Combine these results to find the final sum:
$\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &20 \\ \end{aligned}$

Therefore, the solution to the problem is $20$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Align place values vertically before adding columns
Technique: Start from units column: 2 + 8 = 10, write 0 and carry 1
Check: Verify by horizontal addition: 12 + 8 = 20 matches vertical result ✓

Common Mistakes

Avoid these frequent errors

Not carrying over when sum exceeds 9
Don't write 10 in the units column = wrong answer like 120! When adding digits gives 10 or more, you must carry the tens digit to the next column. Always write only the units digit and carry the rest.

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 line up the numbers vertically?

Aligning by place value ensures you're adding units to units and tens to tens! If numbers aren't lined up properly, you'll add the wrong digits together.

What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and 'carry' the tens digit to the next column on the left. Think of it as borrowing in reverse!

Do I always start from the right side?

Yes! Always start from the rightmost column (units place) and work left. This ensures you handle any carrying correctly as you move to bigger place values.

What if there's no number in one column?

Treat empty spaces as zero. In this problem, there's no tens digit for 8, so we imagine it as 08, making the tens column 1 + 0 = 1 (plus our carried 1).

How can I check if my answer is right?

Use horizontal addition as a check: $12 + 8 = 20$ . You can also try adding in reverse: $8 + 12 = 20$ . Both should match your vertical result!

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