Solve Vertical Addition: 7256 + 1967 Step-by-Step

Q: What does 'carry over' actually mean?

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

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

You start from the ones place (rightmost) because any carrying affects the next column to the left. If you started from the left, you'd mess up your carrying!

Q: What if I have more than one digit to carry?

You can only carry one digit at a time in regular addition. The maximum you'll ever carry is 1, since the largest single-digit sum is 9 + 9 = 18.

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

Try these methods: Add the numbers in reverse orderUse a calculator to verifyEstimate: 7256 + 1967 should be close to 7000 + 2000 = 9000

Q: What if the numbers have different amounts of digits?

No problem! Just align them by place value on the right side. Treat missing digits as zeros. For example, 123 + 45 becomes 123 + 045.

Q: Can I add from left to right instead?

While possible, it's much harder because you have to keep track of carries mentally. The standard right-to-left method is more reliable and less error-prone.

Vertical Addition with Carrying

$\begin{aligned} &7256 \\ +& \\ &1967\\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 Combine two digits at a time. Ready?

00:13 First, ones with ones. Let's do it!

00:17 Write down the ones, carry one to the tens place.

00:21 Now, tens with tens. Remember, add that one!

00:25 Write the tens, and carry one to hundreds.

00:29 Next, combine hundreds with hundreds. Add the one.

00:34 Write down the hundreds, carry one to thousands.

00:39 Finally, combine thousands with thousands. Add one.

00:44 Write down the thousands.

00:47 Great job! That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &7256 \\ +& \\ &1967\\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will apply vertical addition:

Let's add the numbers 7256 and 1967 by arranging them in a column:

First, arrange the numbers by place value:

7256

+1967

—

Next, add the rightmost column (units place):
**6 + 7 = 13**. Write down 3 and carry over 1 to the next column (tens place).
Proceed to the tens place:
**5 + 6 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
Now, add the hundreds place:
**2 + 9 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
Finally, add the thousands place:
**7 + 1 = 8**, plus the carry-over 1 gives **9**. Write down 9.

The sum of the numbers is written as:

7256

+1967

—

9223

Therefore, the correct sum of the numbers 7256 and 1967 is $9223$ .

Final Answer

9223

Key Points to Remember

Essential concepts to master this topic

Column Alignment: Align digits by place value before adding
Carrying Method: When sum ≥ 10, write units digit and carry tens to next column
Verification: Check by adding in reverse order: 1967 + 7256 = 9223 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't write down the full two-digit sum like 13 in one column = wrong place values! This creates numbers like 91313 instead of 9223. Always carry the tens digit to the next 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' actually mean?

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

Why do I start adding from the right side?

You start from the ones place (rightmost) because any carrying affects the next column to the left. If you started from the left, you'd mess up your carrying!

What if I have more than one digit to carry?

You can only carry one digit at a time in regular addition. The maximum you'll ever carry is 1, since the largest single-digit sum is 9 + 9 = 18.

How can I check if my answer is correct?

Try these methods:

Add the numbers in reverse order
Use a calculator to verify
Estimate: 7256 + 1967 should be close to 7000 + 2000 = 9000

What if the numbers have different amounts of digits?

No problem! Just align them by place value on the right side. Treat missing digits as zeros. For example, 123 + 45 becomes 123 + 045.

Can I add from left to right instead?

While possible, it's much harder because you have to keep track of carries mentally. The standard right-to-left method is more reliable and less error-prone.

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