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

00:00 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

00:12 Combine tens with tens

00:14 Place tens in tens, and add 1 to hundreds

00:19 Combine hundreds with hundreds, and place in hundreds

00:29 Combine thousands with thousands

00:33 Place thousands in thousands, and add 1 to tens of thousands

00:41 Combine tens of thousands with tens of thousands

00:45 Place in tens of thousands, and add 1 to hundreds of thousands

00:48 Place 0 in the missing digits

00:51 Combine hundreds of thousands with hundreds of thousands, and place

00:55 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

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

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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