Calculate the Sum: 72354 + 29563 Using Column Addition

Q: What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and carry the tens digit to the next column. For example: 5+6=11, so write 1 and carry 1.

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

You start from the ones place (rightmost) because any carry-over affects the next column to the left. This way, you handle all carries in the correct order.

Q: What if I get confused about which numbers to carry?

Write small carry numbers above the next column as reminders. For 5+6=11, write a small '1' above the hundreds column so you remember to add it later.

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

Try adding the numbers in reverse order (29563 + 72354) or use estimation: 72000 + 30000 = 102000, which is close to 101917 ✓

Column Addition with Multiple Carry-Over Operations

$\begin{aligned} &72354\\ +& \\ &29563 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:10 First, we'll combine two digits at a time.

00:14 Let's start by adding the ones digits.

00:18 Put the result in the ones place.

00:21 Next, combine the tens digits.

00:25 Place them in the tens spot, and carry over 1 to the hundreds.

00:29 Now, add the hundreds digits, and put the result in the hundred s place.

00:36 Let's move to the thousands. Add those next.

00:40 Place the result in the thousands place, and carry 1 to the tens of th ousands.

00:48 Now, add the tens of thousands together.

00:52 Put that result in the tens of thousands, and carry 1 to the hun dreds of thousands.

00:58 Fill in any missing digits with zero.

01:02 Finally, add the hundreds of thousands, and place the result.

01:07 And that's how we solve it! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &72354\\ +& \\ &29563 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will add the two numbers using vertical addition:

Step 1: Write the numbers vertically, aligning them by their place values:
$\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 7 & 2 & 3 & 5 & 4 \\ + & & 2 & 9 & 5 & 6 & 3 \\ \hline \end{array}$
Step 2: Add the digits in each column starting from the rightmost (units) column:

Units place: $4 + 3 = 7$
Tens place: $5 + 6 = 11$ . Write 1 and carry over 1 to the hundreds place.
Hundreds place: $3 + 5 + 1 = 9$ (including the carry-over).
Thousands place: $2 + 9 = 11$ . Write 1 and carry over 1 to the ten-thousands place.
Ten-thousands place: $7 + 2 + 1 = 10$ (including the carry-over). Write 0 and carry over 1.

Step 3: Write down the complete sum:

$\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & 1 & 0 & 1 & 9 & 1 & 7 \\ \hline \end{array}$

Adding all values gives us the final sum.

Therefore, the sum of 72354 and 29563 is $101917$ .

Final Answer

101917

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers with digits in correct place value columns
Technique: Add column by column: 5+6=11, write 1 carry 1
Check: Verify by adding left to right: 101917 has 6 digits ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 11 in the tens place when 5+6=11 = wrong place values! This creates numbers with impossible digit values. 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 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and carry the tens digit to the next column. For example: 5+6=11, so write 1 and carry 1.

Why do I start adding from the right side?

You start from the ones place (rightmost) because any carry-over affects the next column to the left. This way, you handle all carries in the correct order.

What if I get confused about which numbers to carry?

Write small carry numbers above the next column as reminders. For 5+6=11, write a small '1' above the hundreds column so you remember to add it later.

How can I check if my addition is correct?

Try adding the numbers in reverse order (29563 + 72354) or use estimation: 72000 + 30000 = 102000, which is close to 101917 ✓

What happens if I have to carry from the leftmost column?

When the leftmost digits create a carry (like 7+2+1=10), you write the full result. The '1' becomes a new leftmost digit, making your answer longer than the original numbers.

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