Calculate the Sum: 19785 + 30406 Using Column Addition

Q: What does 'carry over' mean exactly?

When you add two digits and get 10 or more, you write down the ones digit and 'carry' the tens digit to the next column on the left. 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 carrying affects the column to the left. If you started from the left, you'd have to go back and fix your work when you carry.

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

Try these methods:Add in reverse order (second number first)Estimate: 19785 ≈ 20000, 30406 ≈ 30000, so answer should be around 50000Subtract: 50191 - 19785 should equal 30406

Q: What if the numbers have different amounts of digits?

No problem! Just align them by place value (ones under ones, tens under tens, etc.). You can imagine zeros in the empty spaces. For example, treat 19785 as having a zero in the hundred-thousands place.

Column Addition with Carrying

$\begin{aligned} &19785\\ +& \\ &30406 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem step by step.

00:11 Start by combining two digits at a time.

00:14 First, combine the ones with the ones.

00:18 Place the result in the ones column. Add one to the tens.

00:23 Next, combine the tens with the tens.

00:27 Add one to your calculation. Place the tens in the tens column.

00:31 Now, combine the hundreds with the hundreds.

00:35 Place the result in the hundreds column. Add one to the thousands.

00:39 Combine the thousands with the thousands.

00:42 Remember to add one to your calculation, then place it in the thousands.

00:47 Finally, combine and place the tens of thousands correctly.

00:51 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &19785\\ +& \\ &30406 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Align the two numbers, 19785 and 30406, for vertical addition.
Step 2: Add the numbers column by column, starting from the rightmost digit.
Step 3: Carry over any value greater than 9 to the next column on the left.

Now, let's work through each step:

Step 1: Align the numbers:
$\begin{array}{c} 19785 \\ +30406 \\ \hline \end{array}$

Step 2: Add the columns starting from the right:

Rightmost column (ones): $5 + 6 = 11$ . Write down $1$ , carry over $1$ .
Tens column: $8 + 0 = 8$ , plus the carry over $1$ gives $9$ .
Hundreds column: $7 + 4 = 11$ . Write down $1$ , carry over $1$ .
Thousands column: $9 + 0 = 9$ , plus the carry over $1$ gives $10$ . Write down $0$ , carry over $1$ .
Ten-thousands column: $1 + 3 = 4$ , plus the carry over $1$ gives $5$ .
Assembling these results, we have the sum of $50191$ .

Therefore, the solution to the problem is $\boxed{50191}$ .

Final Answer

50191

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers vertically with digits in proper place value columns
Technique: Add right to left; when sum > 9, write ones digit and carry tens
Check: Verify by adding left to right or estimating: 20000 + 30000 = 50000 ✓

Common Mistakes

Avoid these frequent errors

Not carrying properly when column sum exceeds 9
Don't just write the full sum in one column like writing '11' in the ones place = wrong place values! This creates numbers with invalid digits. Always write only 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 'carry over' mean exactly?

When you add two digits and get 10 or more, you write down the ones digit and 'carry' the tens digit to the next column on the left. 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 carrying affects the column to the left. If you started from the left, you'd have to go back and fix your work when you carry.

What if I forget to add the carried number?

Your answer will be wrong! Always remember that a carried number is an extra digit to add in the next column. Write small carry numbers above the columns to help you remember.

How can I check if my addition is correct?

Try these methods:

Add in reverse order (second number first)
Estimate: 19785 ≈ 20000, 30406 ≈ 30000, so answer should be around 50000
Subtract: 50191 - 19785 should equal 30406

What if the numbers have different amounts of digits?

No problem! Just align them by place value (ones under ones, tens under tens, etc.). You can imagine zeros in the empty spaces. For example, treat 19785 as having a zero in the hundred-thousands place.

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