Solve Vertical Addition: 74 + 6 Step-by-Step

Q: What does 'carry over' actually mean?

When adding digits gives you 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example, $4 + 6 = 10$ means write 0 and carry the 1.

Q: Why can't I just write 10 in the ones place?

Each place can only hold one digit (0-9). Writing 10 would mean you have two digits in one place, which breaks our number system rules!

Q: How do I check my vertical addition answer?

Try these methods: Add the numbers horizontally to compareAdd in reverse order (6 + 74 instead of 74 + 6)Use estimation to see if your answer makes sense

Q: Do I always start adding from the right side?

Yes, always start from the rightmost column (ones place) and work left. This ensures you handle any carry-overs correctly as you move through each place value.

Vertical Addition with Carry-Over Operations

$\begin{aligned} &74 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's solve this math problem together.

00:05 We will add two-digit numbers one step at a time.

00:10 First, add the ones place digits together.

00:13 Put the ones, and add any carryover to the tens.

00:17 Remember, if you carried over one, keep it in mind.

00:21 If there's an empty place, fill it with zero.

00:25 Now add the tens place digits, including the carryover.

00:29 Put that sum in the tens place.

00:35 And that's how we find the answer to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &74 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers $74$ and $6$ vertically.
Step 2: Begin by adding the digits in the ones place.
Step 3: Move to the tens place and include any carryover.

Let's work through each step:

Step 1: Write the numbers vertically, aligning by place value:
$\begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &~~ \\ \end{aligned}$

Step 2: Add the ones place. The digit in the ones place of 74 is 4, and for 6 is 6. Add them together:
$4 + 6 = 10$ .

Since the result is 10, write down 0 in the ones place and carry over 1 to the tens place.

Step 3: Now, move to the tens place. Add the tens digit from 74, which is 7, and add the 1 carried over from the previous step:
$7 + 1 = 8$ .

This results in:
$\begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &80 \\ \end{aligned}$

Therefore, the solution to the problem is $80$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Place Value: Always align numbers by ones and tens columns
Technique: When 4 + 6 = 10, write 0 and carry 1
Check: Verify by adding horizontally: 74 + 6 = 80 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 10 directly in the ones place = incorrect 100 result! When digits add to 10 or more, you must write only the ones digit and carry the tens digit to the next column. Always carry over any value 10 or greater.

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' actually mean?

When adding digits gives you 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example, $4 + 6 = 10$ means write 0 and carry the 1.

Why can't I just write 10 in the ones place?

Each place can only hold one digit (0-9). Writing 10 would mean you have two digits in one place, which breaks our number system rules!

What if there's no digit in the tens place to add the carry to?

If you're adding numbers like 9 + 7 with no tens place, the carried 1 becomes your tens digit. So $9 + 7 = 16$ (write 6, carry 1 to create the tens place).

How do I check my vertical addition answer?

Try these methods:

Add the numbers horizontally to compare
Add in reverse order (6 + 74 instead of 74 + 6)
Use estimation to see if your answer makes sense

Do I always start adding from the right side?

Yes, always start from the rightmost column (ones place) and work left. This ensures you handle any carry-overs correctly as you move through each place value.

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