Solve 429 + 5982 Using Place Value Conversion Table

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: $ 9+2=11 $ means write 1 and carry 1.

Q: Why do I need to align the numbers by place value?

Place value alignment ensures you're adding ones to ones, tens to tens, etc. Without proper alignment, you might accidentally add a tens digit to a ones digit, giving completely wrong answers!

Q: What if I forget to carry a number?

Your final answer will be wrong! Always double-check each column where the sum is 10 or greater. Write the ones digit down and don't forget to add the tens digit to the next column.

Q: Can I add from left to right instead?

It's much harder that way! Adding from right to left (ones, tens, hundreds, thousands) makes carrying easier because you handle smaller numbers first and build up naturally.

Q: How do I know if my final answer is correct?

Try adding the numbers in reverse order: $ 5982+429 $ should give the same result as $ 429+5982 $. You can also estimate: 400+6000 ≈ 6400, so 6411 makes sense!

Column Addition with Carrying Conversions

Solve the following equation using the table below:

$429+5982=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation using the table below:

$429+5982=$

Step-by-step solution

To solve the addition problem $429 + 5982$ , we will break it down into basic addition steps using place value alignment:

First, write the numbers on top of each other in a column, aligning by place value (ones, tens, hundreds, thousands).
Start adding from the rightmost column (ones):

Ones column: $9 + 2 = 11$ ; write 1 in the ones place and carry over 1 to the tens place.
Tens column: $2 + 8 + 1 \text{ (carry)} = 11$ ; write 1 in the tens place and carry over 1 to the hundreds place.
Hundreds column: $4 + 9 + 1 \text{ (carry)} = 14$ ; write 4 in the hundreds place and carry over 1 to the thousands place.
Thousands column: $5 + 1 \text{ (carry)} = 6$ ; write 6 in the thousands place.

Thus, the sum of the addition $429 + 5982$ is computed by combining all the resulting digits after addition and carry-over adjustments.

Therefore, the solution to the problem is $6411$ .

Final Answer

$6411$

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up digits by place value columns correctly
Carrying: When sum exceeds 9, write ones digit and carry tens: $9+2=11$ gives 1, carry 1
Check: Verify final answer by adding in reverse order: $5982+429=6411$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add carried numbers
Don't just add the original digits in each column and forget the carry = wrong totals like 5411 instead of 6411! This happens when you carry the 1 but don't include it in the next column's addition. Always add the carry to the next column's sum.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct answer:

$693+705=\text{ ?}$

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: $9+2=11$ means write 1 and carry 1.

Why do I need to align the numbers by place value?

Place value alignment ensures you're adding ones to ones, tens to tens, etc. Without proper alignment, you might accidentally add a tens digit to a ones digit, giving completely wrong answers!

What if I forget to carry a number?

Your final answer will be wrong! Always double-check each column where the sum is 10 or greater. Write the ones digit down and don't forget to add the tens digit to the next column.

Can I add from left to right instead?

It's much harder that way! Adding from right to left (ones, tens, hundreds, thousands) makes carrying easier because you handle smaller numbers first and build up naturally.

How do I know if my final answer is correct?

Try adding the numbers in reverse order: $5982+429$ should give the same result as $429+5982$ . You can also estimate: 400+6000 ≈ 6400, so 6411 makes sense!

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