Add Three-Digit Numbers: Solving 822 + 178

Q: What does 'carry over' actually mean?

When digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. It's like trading 10 ones for 1 ten!

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

We start from the units place (rightmost) because any carrying affects the column to the left. If we started left, we'd have to redo our work when carries happen!

Q: What if I carry multiple times in one problem?

That's completely normal! In 822 + 178, we carry three times. Just handle one column at a time: add the digits, add any carry from the right, then carry left if needed.

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

Try adding the numbers in reverse order: 178 + 822. You should get the same answer. Or subtract one original number from your sum to get the other original number!

Q: What happens when carrying creates a new digit?

When the leftmost column needs to carry (like $8 + 1 + 1 = 10$), you create a new thousands place. That's why 822 + 178 becomes the 4-digit number 1000!

Three-Digit Addition with Multiple Carrying

$\begin{aligned} &822 \\ +& \\ &178 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 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 1 to tens

00:12 Combine tens with tens, remember to add 1 to the calculation

00:16 Place tens in tens, add 1 to hundreds

00:20 Combine hundreds with hundreds, remember to add 1

00:24 Place hundreds in hundreds, and add 1 to thousands

00:27 Place 0 in the missing digits

00:31 Combine thousands with thousands, remember to add 1

00:34 Place in thousands

00:37 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

$\begin{aligned} &822 \\ +& \\ &178 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers vertically by their place values.
The numbers are given as:

$\begin{aligned} &822 \\ + &178 \\ \end{aligned}$

Step 2: Add the digits from right to left, starting with the units place.

Units place addition:
$2 + 8 = 10$

We place $0$ in the units place and carry over $1$ to the tens place.

Step 3: Add the digits in the tens place, including the carry-over.

$2 + 7 = 9$ , plus the carried over $1$ :
$9 + 1 = 10$

We place $0$ in the tens place and carry over $1$ to the hundreds place.

Step 4: Add the digits in the hundreds place, including the carry-over.

$8 + 1 = 9$ , plus the carried over $1$ :
$9 + 1 = 10$

Place $0$ in the hundreds place and carry over $1$ to the next place, creating a new thousands place digit.

Resulting sum:

$\begin{aligned} &1000 \end{aligned}$

Therefore, the solution to the problem is $1000$ .

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers vertically by place value positions
Technique: Add right to left: $2 + 8 = 10$ , carry the 1
Check: Verify each column adds correctly with carries: 822 + 178 = 1000 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 10 in one column = wrong place values! When 2 + 8 = 10, you can't write '10' in the units place. Always write the ones digit (0) and carry the tens digit (1) to the next column.

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

What does 'carry over' actually mean?

When digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. It's like trading 10 ones for 1 ten!

Why do I start adding from the right side?

We start from the units place (rightmost) because any carrying affects the column to the left. If we started left, we'd have to redo our work when carries happen!

What if I carry multiple times in one problem?

That's completely normal! In 822 + 178, we carry three times. Just handle one column at a time: add the digits, add any carry from the right, then carry left if needed.

How can I check if my addition is correct?

Try adding the numbers in reverse order: 178 + 822. You should get the same answer. Or subtract one original number from your sum to get the other original number!

What happens when carrying creates a new digit?

When the leftmost column needs to carry (like $8 + 1 + 1 = 10$ ), you create a new thousands place. That's why 822 + 178 becomes the 4-digit number 1000!

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