Solve Three-Digit Addition: 548 + 459 in Vertical Format

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

When adding digits in a column gives you 10 or more, you write the units digit in that column and carry the tens digit to the next column on the left. For example: 8 + 9 = 17, so write 7 and carry 1.

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

We start from the units column because any carrying affects the next column to the left. If we started from the left, we'd miss the carried amounts from the right columns!

Q: How do I know if my final answer is correct?

You can check by adding in reverse: $ 1007 - 459 = 548 $. If you get back to your original first number, your addition is correct!

Q: What happens when the hundreds column needs carrying too?

When hundreds carrying happens (like $ 5 + 4 + 1 = 10 $), you create a new thousands place. Write 0 in hundreds and 1 in the new thousands column, giving you a 4-digit answer.

Column Addition with Carrying Regrouping

$\begin{aligned} &548 \\ +& \\ &459 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 we'll place

00:06 Let's start by adding units with units

00:09 Place the units, add 1 to the tens

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

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

00:22 Add hundreds with hundreds, remember to add 1

00:26 Place hundreds in hundreds, and add 1 to thousands

00:30 Place 0 in the missing digits

00:34 Add thousands with thousands, remember to add 1

00:37 Place in thousands

00:41 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

$\begin{aligned} &548 \\ +& \\ &459 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Add the units digits of both numbers.
Step 2: Handle any regrouping if necessary and add the tens digits.
Step 3: Handle any regrouping if necessary and add the hundreds digits.

Now, let's work through each step:

Step 1: Add the units digits of both numbers:
$8 + 9 = 17$ . Here, 7 is placed in the units place, and 1 is carried over to the tens column.

Step 2: Add the tens digits along with the carry-over:
$4 + 5 + 1 = 10$ . Here, 0 is placed in the tens place, and 1 is carried over to the hundreds column.

Step 3: Add the hundreds digits along with the carry-over:
$5 + 4 + 1 = 10$ . Here, 0 is placed in the hundreds place, and 1 is carried over to the thousands column.

The final sum is $1007$ , where 1 is now the digit in the thousands place.

Therefore, the solution to the problem is $1007$ .

Final Answer

1007

Key Points to Remember

Essential concepts to master this topic

Rule: Add columns right to left, carrying when sum exceeds 9
Technique: Units: 8 + 9 = 17, write 7 carry 1
Check: Final answer 1007 has correct place values in all positions ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over digits when sum exceeds 9
Don't write 17 in the units column or ignore the carry = wrong final answer! When 8 + 9 = 17, you must write 7 and carry the 1 to the next column. Always carry the tens digit when any column sum is 10 or greater.

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

What does it mean to 'carry' a number?

When adding digits in a column gives you 10 or more, you write the units digit in that column and carry the tens digit to the next column on the left. For example: 8 + 9 = 17, so write 7 and carry 1.

Why do we start adding from the right side?

We start from the units column because any carrying affects the next column to the left. If we started from the left, we'd miss the carried amounts from the right columns!

What if I need to carry multiple times in one problem?

That's completely normal! In this problem, we carried from units to tens and from tens to hundreds. Just handle each carry one column at a time as you work left.

How do I know if my final answer is correct?

You can check by adding in reverse: $1007 - 459 = 548$ . If you get back to your original first number, your addition is correct!

What happens when the hundreds column needs carrying too?

When hundreds carrying happens (like $5 + 4 + 1 = 10$ ), you create a new thousands place. Write 0 in hundreds and 1 in the new thousands column, giving you a 4-digit answer.

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