Solve Addition: 66543 + 52456 Using Vertical Method

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 to the left. For example: $6 + 5 = 11$ means write 1 and carry 1.

Q: Why do we start from the rightmost column?

We start from the units place (rightmost) because any carrying affects the column to the left. Working left-to-right would mess up our carrying and give wrong answers!

Q: What if I have to carry multiple times?

That's totally normal! Just handle one column at a time. Add the digits in that column plus any carry from the previous column, then carry again if needed.

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

Try these methods: Add the numbers in reverse order (52456 + 66543)Estimate by rounding: 67000 + 52000 = 119000Use subtraction: 118999 - 66543 should equal 52456

Vertical Addition with Multi-digit Carrying

$\begin{aligned} &66543\\ +& \\ &52456 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 place

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

00:09 Place the ones

00:12 Combine tens with tens, and place in tens

00:16 Combine hundreds with hundreds

00:19 Place hundreds in hundreds, and add 1 to thousands

00:23 Combine thousands with thousands, remember to add 1 to the calculation

00:29 Place in thousands

00:33 Combine tens of thousands with tens of thousands

00:37 Place in tens of thousands, and add 1 to hundreds of thousands

00:40 Place 0 in the missing digits

00:43 Combine hundreds of thousands with hundreds of thousands, and place

00:48 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

$\begin{aligned} &66543\\ +& \\ &52456 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Align the numbers for vertical addition as follows:

$\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 6 & 6 & 5 & 4 & 3 \\ + & 5 & 2 & 4 & 5 & 6 \\ \hline \end{array}$

Step 2: Perform the addition from the rightmost digit (units place):

Units place: $3 + 6 = 9$
Tens place: $4 + 5 = 9$
Hundreds place: $5 + 4 = 9$
Thousands place: $6 + 2 = 8$
Ten-thousands place: $6 + 5 = 11$
Write 1 in the ten-thousands place and carry over 1 to the next column.
Since there are no more columns left to add the carry over, the final digit in the ten-thousands place is 11.

The final result is:

$\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 1 & 1 & 8 & 9 & 9 & 9 \\ \end{array}$

Therefore, the sum of 66543 and 52456 is $118999$ .

Final Answer

118999

Key Points to Remember

Essential concepts to master this topic

Rule: Always add from right to left, column by column
Technique: When sum exceeds 9, carry 1 to next column: $6 + 5 = 11$ becomes 1 carry, 1 write
Check: Verify by adding in reverse or estimating: $67000 + 52000 = 119000$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when digits sum to 10 or more
Don't just write down sums like 11 or 13 directly in your answer = wrong final result! When digits add to 10 or more, you must carry the tens digit to the next column. Always write only the units digit and carry the tens digit left.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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 to the left. For example: $6 + 5 = 11$ means write 1 and carry 1.

Why do we start from the rightmost column?

We start from the units place (rightmost) because any carrying affects the column to the left. Working left-to-right would mess up our carrying and give wrong answers!

What if I have to carry multiple times?

That's totally normal! Just handle one column at a time. Add the digits in that column plus any carry from the previous column, then carry again if needed.

How can I check if my answer is correct?

Try these methods:

Add the numbers in reverse order (52456 + 66543)
Estimate by rounding: 67000 + 52000 = 119000
Use subtraction: 118999 - 66543 should equal 52456

What if my final answer has more digits than either original number?

That's expected when adding large numbers! The final answer 118999 has 6 digits while both original numbers had only 5 digits. This happens when there's a final carry.

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