Add Four-Digit Numbers: 8472 + 5261 Using Column Method

Q: What does 'carry over' mean in addition?

When adding digits gives you 10 or more, you write the ones digit and 'carry' the tens digit to the next column. For example, $7 + 6 = 13$, so write 3 and carry 1 to the hundreds column.

Q: Why do I start adding from the right side?

We start from the units column (rightmost) because any carries need to move left to the next higher place value. Starting from the left would mean redoing work when carries happen!

Q: How do I know if I aligned the numbers correctly?

Make sure digits with the same place value are in the same column: units under units, tens under tens, hundreds under hundreds, and thousands under thousands.

Q: What if I get confused with the carrying?

Write small carry numbers above the next column to remember them. In this problem, write small '1' above the hundreds column after getting $7 + 6 = 13$.

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

Estimation method: Round both numbers and add mentally. $8500 + 5300 = 13800$, which is close to our answer 13733. You can also add the numbers in a different order to verify!

Column Addition with Four-Digit Numbers

$\begin{aligned} &8472\\ +& \\ &5261 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 We'll combine two digits at a time.

00:12 Start by adding the ones place with the ones.

00:16 Put that result in the ones place.

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

00:22 Place that in the tens spot and carry over one to the hundreds.

00:27 Add the hundreds together and don’t forget the one you carried.

00:31 Place this total in the hundreds column.

00:34 Now, add up the thousands with the thousands.

00:39 Put this in the thousands place and carry one to the tens of thousands.

00:44 Fill any missing spots with zero.

00:47 Finally, add tens of thousands to tens of thousands.

00:51 And there you have it, we've solved the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &8472\\ +& \\ &5261 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Align the numbers by their place values.
Step 2: Add the digits starting from the rightmost column.
Step 3: Handle any carryovers properly.
Step 4: Write down the final result.

Now, let's work through each step:

Step 1: Align the numbers:

$8472$
$+ 5261$
$\_\_\_\_\_\_\_\_\_$

Step 2: Begin adding the digits starting from the rightmost side:

Units column: $2 + 1 = 3$ .

Tens column: $7 + 6 = 13$ . Write $3$ and carry over $1$ .

Hundreds column: $4 + 2 + 1 \,(carry) = 7$ .

Thousands column: $8 + 5 = 13$ . Write $3$ and carry over $1$ .

Step 3: Handle the extra thousands place from the carryover: $1$ .

Thus, the full addition with carryovers corrected is:

$8472$
$+ 5261$
$\_\_\_\_\_\_\_\_=\_13733$

Therefore, the correct solution to the problem is $13733$ .

Final Answer

13733

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with digits properly aligned
Technique: Start from rightmost column: 2 + 1 = 3, then move left
Check: Verify by adding in reverse or estimating: 8500 + 5300 ≈ 13800 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't ignore carries like writing 13 in the tens place = wrong digits in wrong places! When 7 + 6 = 13, you must write 3 and carry the 1 to the next column. Always carry the tens digit to the left column and write only the units 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

What does 'carry over' mean in addition?

When adding digits gives you 10 or more, you write the ones digit and 'carry' the tens digit to the next column. For example, $7 + 6 = 13$ , so write 3 and carry 1 to the hundreds column.

Why do I start adding from the right side?

We start from the units column (rightmost) because any carries need to move left to the next higher place value. Starting from the left would mean redoing work when carries happen!

How do I know if I aligned the numbers correctly?

Make sure digits with the same place value are in the same column: units under units, tens under tens, hundreds under hundreds, and thousands under thousands.

What if I get confused with the carrying?

Write small carry numbers above the next column to remember them. In this problem, write small '1' above the hundreds column after getting $7 + 6 = 13$ .

How can I check if my answer is right?

Estimation method: Round both numbers and add mentally. $8500 + 5300 = 13800$ , which is close to our answer 13733. You can also add the numbers in a different order to verify!

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