Calculate the Sum: Adding 8974 and 264 in Vertical Format

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

When a column adds up to 10 or more, you write the units digit and carry the tens digit to the next column. For example, 7 + 6 = 13, so write 3 and carry 1.

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

We start from the units column because that's where carrying begins! If you start from the left, you won't know what to carry over.

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

That's fine! Just imagine invisible zeros in front of the shorter number. In this problem, 264 is really 0264 when aligned with 8974.

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

Try adding the numbers in reverse order (264 + 8974) or use subtraction: 9238 - 264 should equal 8974!

Q: What if I need to carry more than once in the same problem?

That's normal! In this problem, we carried from tens to hundreds and from hundreds to thousands. Just take it one column at a time.

Vertical Addition with Carrying

$\begin{aligned} &8974 \\ +& \\ &~~264 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 write

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

00:09 Write down the ones

00:11 Add tens with tens

00:14 Write down tens in tens, add 1 to hundreds

00:19 Add hundreds with hundreds, remember to add 1

00:22 Write hundreds in hundreds, and add 1 to thousands

00:26 Write 0 in the missing digits

00:30 Add thousands with thousands, remember to add 1

00:34 Write 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

$\begin{aligned} &8974 \\ +& \\ &~~264 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Arrange the numbers vertically with 8974 on top and 264 below it.
Step 2: Add the numbers column by column, starting from the rightmost (units) column.
Step 3: Record the sum below the line, carrying over wherever necessary.

Let's perform the addition:

Step 1: Arrange the numbers vertically.

$\begin{array}{c} 8974 \\ +264 \\ \underline{\phantom{776}} \\ \end{array}$

Step 2: Begin adding from the rightmost column (units):

Units digit: $4 + 4 = 8$ , so write 8 in the units place.
Tens digit: $7 + 6 = 13$ , write 3 and carry over 1 to the hundreds column.
Hundreds digit: $9 + 2 + 1 = 12$ , write 2 and carry over 1 to the thousands column.
Thousands digit: $8 + 1 = 9$ , write 9.

Step 3: Write the final result:

$\begin{array}{c} 8974 \\ +264 \\ \underline{9238} \\ \end{array}$

Therefore, the solution to the problem is $9238$ .

Final Answer

9238

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack digits by place value with units column aligned
Technique: Add column by column: 7 + 6 = 13, write 3 carry 1
Check: Verify by adding in different order: 264 + 8974 = 9238 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add carried digits to the next column
Don't forget carried numbers like writing 2 instead of 12 when adding hundreds = wrong total! This happens when you carry but forget to add it to the next column. Always add the carried digit plus the digits in that 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 'carry over' mean in addition?

When a column adds up to 10 or more, you write the units digit and carry the tens digit to the next column. For example, 7 + 6 = 13, so write 3 and carry 1.

Why do we start adding from the right side?

We start from the units column because that's where carrying begins! If you start from the left, you won't know what to carry over.

What if the numbers have different amounts of digits?

That's fine! Just imagine invisible zeros in front of the shorter number. In this problem, 264 is really 0264 when aligned with 8974.

How can I check if my addition is correct?

Try adding the numbers in reverse order (264 + 8974) or use subtraction: 9238 - 264 should equal 8974!

What if I need to carry more than once in the same problem?

That's normal! In this problem, we carried from tens to hundreds and from hundreds to thousands. Just take it one column at a time.

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