Solve Vertical Addition: 871 + 36 Step-by-Step

Q: Why do I need to align the numbers vertically?

Proper alignment ensures you add the correct place values! Units go under units, tens under tens. If 36 isn't aligned properly under 871, you'll add wrong digits together.

Q: What does 'carry over' mean exactly?

When a column sum is 10 or greater, you write the units digit and carry the tens digit to the next column. For example: $7 + 3 = 10$ means write 0 and carry 1.

Q: How do I remember which direction to carry?

Always carry to the left (to the next higher place value). Think of it as moving from smaller to larger place values: units → tens → hundreds.

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

Use horizontal addition as a check: $871 + 36$. You can also use estimation: 871 is close to 870, and $870 + 36 = 906$, so 907 makes sense!

Vertical Addition with Carrying Procedure

$\begin{aligned} &871 \\ +& \\ &~~36 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this math problem

00:07 Consider pairing two digits, then place them correctly.

00:12 First, let's add the ones digit with the ones digit.

00:16 Place the sum in the ones place.

00:19 Next, add the tens digit with the tens digit.

00:23 Put the result in the tens place and carry over one to the hundre ds.

00:28 Make sure to use a zero for any missing digit places.

00:32 Finally, add the hundreds digit with the hundreds digit, don't forg et the carry over, and place the re sult in the hundreds place.

00:40 And that's how we find the solution to this problem. Great jo b!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &871 \\ +& \\ &~~36 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, let's perform vertical addition:

Step 1: Align the Numbers
$871$
+ $36$
$\underline{\phantom{7777}}$
Step 2: Add the Units
Add the digits in the unit’s place: $1 + 6 = 7$ . Write 7 in the unit’s position.
Step 3: Add the Tens
Add the digits in the tens place: $7 + 3 = 10$ . Write 0 in the tens position and carry over 1 to the hundreds.
Step 4: Add the Hundreds
Add the digits in the hundreds place, including the carry over: $8 + 1 = 9$ .

By combining these steps, the complete sum is $907$ .

Therefore, the solution to this problem is $\boxed{907}$ .

Final Answer

907

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with units directly aligned
Technique: Add column by column: $7 + 3 = 10$ , carry the 1
Check: Verify by adding horizontally: $871 + 36 = 907$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 10 in the tens place when $7 + 3 = 10$ = wrong answer 917! This ignores place value rules and creates impossible digits. Always write 0 and carry the 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

Why do I need to align the numbers vertically?

Proper alignment ensures you add the correct place values! Units go under units, tens under tens. If 36 isn't aligned properly under 871, you'll add wrong digits together.

What does 'carry over' mean exactly?

When a column sum is 10 or greater, you write the units digit and carry the tens digit to the next column. For example: $7 + 3 = 10$ means write 0 and carry 1.

How do I remember which direction to carry?

Always carry to the left (to the next higher place value). Think of it as moving from smaller to larger place values: units → tens → hundreds.

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

Just bring down the digit! In this problem, since 36 has no hundreds digit, we only add $8 + 1$ (the carried 1) to get 9 in the hundreds place.

How can I check if my answer is correct?

Use horizontal addition as a check: $871 + 36$ . You can also use estimation: 871 is close to 870, and $870 + 36 = 906$ , so 907 makes sense!

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