Solve Three-Digit Addition: 826 + 178 in Vertical Format

Q: What does it mean to 'carry over' a number?

When a column adds up to 10 or more, you write down the ones digit and move (carry) the tens digit to the next column on the left. Think of it as exchanging 10 ones for 1 ten!

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

Proper alignment ensures you're adding ones to ones, tens to tens, hundreds to hundreds. Misaligned numbers lead to adding wrong place values together, giving incorrect answers.

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

Three ways to verify:Add the numbers in reverse order (178 + 826)Use estimation: 800 + 200 ≈ 1000 (close to 1004 ✓)Subtract one addend from your sum: 1004 - 826 = 178 ✓

Q: Is there a pattern to when I need to carry?

Yes! You carry whenever the sum of a column is 10 or greater. In this problem: 6+8=14 (carry), 2+7+1=10 (carry), 8+1+1=10 (carry to make thousands place).

Three-Digit Addition with Regrouping

$\begin{aligned} &826 \\ +& \\ &178 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 Think about combining two digits each time.

00:13 First, multiply the ones digit by the ones digit.

00:17 Put the result in the ones place, then add one to the tens.

00:22 Next, multiply the tens digit by the tens digit. Don't forget to add one!

00:29 Put the result in the tens place and add one to the hundreds.

00:34 Now, multiply the hundreds digit by the hundreds digit, and remember to add one.

00:40 Place the result in the hundreds place, and add one to the thousands.

00:45 If there are missing digits, just place zeros there.

00:50 Finally, multiply the thousands digit by the thousands digit, and add one.

00:55 Put the result in the thousands place.

00:58 And that's how we find the solution! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &826 \\ +& \\ &178 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem of adding $826$ and $178$ using vertical addition, we proceed as follows:

First, we align the numbers vertically, ensuring that digits are in their respective places:

$\begin{array}{c} & 8 & 2 & 6 \\ + & 1 & 7 & 8 \\ \hline \end{array}$

Step 1: Add the units (rightmost) column: $6 + 8 = 14$ . Place the $4$ in the units column of the result and carry over the $1$ to the tens column.
Step 2: Add the tens column: $2 + 7 = 9$ and add the carried over $1$ : $9 + 1 = 10$ . Place $0$ in the tens column of the result and carry over the $1$ to the hundreds column.
Step 3: Add the hundreds column: $8 + 1 = 9$ and add the carried over $1$ : $9 + 1 = 10$ . Write down the entire sum, $10$ , in the hundreds and beyond place.

The resulting sum is $1004$ .

Thus, the solution to the problem is $1004$ .

Final Answer

1004

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack digits in proper place value columns
Regrouping: When column sum ≥ 10, carry 1 to next column (6+8=14, write 4, carry 1)
Verification: Check by adding in reverse order: 178 + 826 = 1004 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sums exceed 9
Don't just write down the full sum like 14 in the units column = wrong answer! This ignores place value rules and creates numbers with impossible digits. Always write the ones digit and carry the tens digit to the next column.

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 it mean to 'carry over' a number?

When a column adds up to 10 or more, you write down the ones digit and move (carry) the tens digit to the next column on the left. Think of it as exchanging 10 ones for 1 ten!

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

Proper alignment ensures you're adding ones to ones, tens to tens, hundreds to hundreds. Misaligned numbers lead to adding wrong place values together, giving incorrect answers.

What if I forget to add a carried number?

Always check each column carefully! Write small carry numbers above the next column as reminders. Missing a carry typically makes your answer 10 or 100 too small.

How can I check if my addition is correct?

Three ways to verify:

Add the numbers in reverse order (178 + 826)
Use estimation: 800 + 200 ≈ 1000 (close to 1004 ✓)
Subtract one addend from your sum: 1004 - 826 = 178 ✓

Is there a pattern to when I need to carry?

Yes! You carry whenever the sum of a column is 10 or greater. In this problem: 6+8=14 (carry), 2+7+1=10 (carry), 8+1+1=10 (carry to make thousands place).

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