Solve Five-Digit Addition: 35612 + 44675 Using Vertical Format

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

When two digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. For example: 6 + 6 = 12, so write 2 and carry 1.

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

We start from the ones place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd have to redo our work when carries change previous sums!

Q: How do I make sure my numbers are lined up correctly?

Line up the ones digits on the rightMake sure each column has digits from the same place valueUse graph paper or draw lines to keep columns straight

Q: What if I forget to add a carried number?

Your final answer will be wrong by exactly the amount you forgot. In this problem, forgetting to add the carried 1 in the thousands place gives 79287 instead of 80287 - off by 1000!

Q: How can I check my addition is correct?

Try these methods:Add in reverse order (44675 + 35612)Estimate first: 36000 + 45000 ≈ 81000, so 80287 makes senseAdd each column again to verify your carries

Q: Why is my answer different from the choices given?

Double-check your carrying and column alignment. Most errors happen when forgetting to carry or misaligning place values. Work through each column slowly and verify each step.

Five-Digit Addition with Column Carrying

$\begin{aligned} &35612\\ +& \\ &44675 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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

00:14 Combine tens with tens, and place in tens

00:17 Combine hundreds with hundreds

00:20 Place hundreds in hundreds, add 1 to thousands

00:25 Combine thousands with thousands, remember to add 1 to the calculation

00:30 Place thousands in thousands, and add 1 to tens of thousands

00:37 Combine tens of thousands with tens of thousands, and place

00:43 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

$\begin{aligned} &35612\\ +& \\ &44675 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use vertical addition, carefully ensuring each digit is correctly placed and carried over if necessary:

Write the numbers on top of each other as such:
35612
+
44675

Begin with the rightmost column (ones place):

Column 1 (Units): $2 + 5 = 7$ . Place 7 below the line.
Column 2 (Tens): $1 + 7 = 8$ . Place 8 below the line.
Column 3 (Hundreds): $6 + 6 = 12$ . The sum is greater than 9, so place 2 below the line and carry over 1 to the next column.
Column 4 (Thousands): $5 + 4 = 9$ , then add the carryover 1 to get 10. Place 0 below the line and carry over 1.
Column 5 (Ten-Thousands): $3 + 4 = 7$ , then add the carryover 1 to get 8. Place 8 below the line.

The complete addition step-by-step is as follows:

35612
+
44675
_____
80287

Therefore, the sum of $35612$ and $44675$ is $80287$ .

Comparing with the choices given, our result matches choice 2.

Thus, the solution to the problem is $80287$ .

Final Answer

80287

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers vertically, matching place values perfectly
Technique: Add right to left: 6 + 6 = 12, write 2, carry 1
Check: Verify each column sum and confirm final answer: 80287 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 12 in the hundreds place when 6 + 6 = 12 = wrong total 791287! The extra digit shifts everything left incorrectly. Always write the ones digit and carry the tens digit to the next column.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

What does it mean to 'carry over' in addition?

When two digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. For example: 6 + 6 = 12, so write 2 and carry 1.

Why do I start adding from the right side?

We start from the ones place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd have to redo our work when carries change previous sums!

How do I make sure my numbers are lined up correctly?

Line up the ones digits on the right
Make sure each column has digits from the same place value
Use graph paper or draw lines to keep columns straight

What if I forget to add a carried number?

Your final answer will be wrong by exactly the amount you forgot. In this problem, forgetting to add the carried 1 in the thousands place gives 79287 instead of 80287 - off by 1000!

How can I check my addition is correct?

Try these methods:

Add in reverse order (44675 + 35612)
Estimate first: 36000 + 45000 ≈ 81000, so 80287 makes sense
Add each column again to verify your carries

Why is my answer different from the choices given?

Double-check your carrying and column alignment. Most errors happen when forgetting to carry or misaligning place values. Work through each column slowly and verify each step.

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