Calculate the Sum: 95781 + 22245 in Vertical Format

Q: Why do I need to line up the digits vertically?

Place value alignment is crucial! The ones must be under ones, tens under tens, etc. If digits aren't properly aligned, you'll add wrong place values together and get an incorrect answer.

Q: What does 'carry over' actually mean?

When a column adds up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. Think of it as 'borrowing' but in reverse!

Q: How do I handle carrying to a new place value?

If your leftmost column creates a carry (like $ 9 + 2 = 11 $), simply write the carried digit as a new leftmost digit. This creates a 6-digit answer from two 5-digit numbers.

Q: Can I add from left to right instead?

It's much harder that way! Starting from the right lets you handle carries naturally. Left-to-right requires estimating carries ahead of time, which often leads to mistakes.

Q: What if I make an error in one column?

One wrong column affects all columns to the left due to carrying! Always double-check each column calculation and verify your carries are correct.

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

Add the numbers horizontally using a calculatorAdd the columns again from scratchEstimate: 95781 ≈ 96000, 22245 ≈ 22000, so answer should be near 118000 ✓

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 combining ones with ones

00:09 Place the ones

00:13 Combine tens with tens

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

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

00:23 Place hundreds in hundreds, and add 1 to thousands

00:27 Combine thousands with thousands, remember to add 1 to the calculation

00:31 Place in thousands

00:34 Combine tens of thousands with tens of thousands

00:39 Place in tens of thousands, and add 1 to hundreds of thousands

00:42 Place 0 in the missing digits

00:46 Combine hundreds of thousands with hundreds of thousands, and place

00:49 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &95781\\ +& \\ &22245 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

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

Step 1: Align the numbers vertically for addition.
Step 2: Add each column starting from the rightmost digit (units) and moving to the left.
Step 3: Record any carry needed for sums exceeding 9.

Let's execute the vertical addition:
Write the numbers aligning each digit according to its place value:

$\begin{array}{c} 95781 \\ +22245 \\ \end{array}$

Step-by-step vertical addition:

Starting with the units place: $1 + 5 = 6$ . Record 6.
Tens place: $8 + 4 = 12$ . Record 2, carry over 1 to the hundreds place.
Hundreds place: $7 + 2 = 9$ , add the carry 1 to get $10$ . Record 0, carry over 1 to the thousands place.
Thousands place: $5 + 2 = 7$ , add the carry 1 to get $8$ . Record 8.
Ten-thousands place: $9 + 2 = 11$ . Record 1 and carry over 1 to the next place.
Since there's no next place, record this final carry in the ten-thousands place: 1.

Therefore, the sum of 95781 and 22245 is:

$\boxed{118026}$

The correct choice in the multiple-choice options is option 2, which matches our calculated sum.

Therefore, the solution to the problem is 118026.

3

Final Answer

118026

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up digits by place value in vertical columns
Technique: Start from rightmost column; $8 + 4 = 12$ , write 2, carry 1
Check: Add horizontally: 95781 + 22245 = 118026 matches vertical result ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't just write the full sum like 12 in the tens column = wrong final answer! When 8 + 4 = 12, you must write 2 and carry the 1 to the next column. Always carry over the tens digit when any column sum is 10 or greater.

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

Why do I need to line up the digits vertically?

+

Place value alignment is crucial! The ones must be under ones, tens under tens, etc. If digits aren't properly aligned, you'll add wrong place values together and get an incorrect answer.

What does 'carry over' actually mean?

+

When a column adds up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. Think of it as 'borrowing' but in reverse!

How do I handle carrying to a new place value?

+

If your leftmost column creates a carry (like $9 + 2 = 11$ ), simply write the carried digit as a new leftmost digit. This creates a 6-digit answer from two 5-digit numbers.

Can I add from left to right instead?

+

It's much harder that way! Starting from the right lets you handle carries naturally. Left-to-right requires estimating carries ahead of time, which often leads to mistakes.

What if I make an error in one column?

+

One wrong column affects all columns to the left due to carrying! Always double-check each column calculation and verify your carries are correct.

How can I check my vertical addition is correct?

+

Add the numbers horizontally using a calculator
Add the columns again from scratch
Estimate: 95781 ≈ 96000, 22245 ≈ 22000, so answer should be near 118000 ✓

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Calculate the Sum: 95781 + 22245 in Vertical Format

Vertical Addition with Multi-digit Carrying

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