Solve Vertical Addition: 746 + 68 Step by Step

Q: Why do I need to align the numbers to the right?

Place value alignment is crucial! The ones must line up with ones, tens with tens, etc. If you align left, you'd be adding hundreds to tens, which gives completely wrong results.

Q: What does 'carry over' mean exactly?

When adding digits gives you 10 or more, the tens digit goes to the next column. Think of it like trading: 14 ones = 1 ten + 4 ones, so you carry that 1 ten to the tens place.

Q: How do I add when one number is missing digits?

Treat missing digits as zero! In 746 + 68, there's no hundreds digit in 68, so it's really 746 + 068. Just add 7 + 0 + any carry for the hundreds place.

Q: Is there a way to check my answer without doing the problem again?

Yes! Use estimation: 746 + 68 is about 750 + 70 = 820. Your answer of 814 is close to 820, so it's reasonable. You can also try subtraction: 814 - 68 should equal 746.

Vertical Addition with Carrying

$\begin{aligned} &746 \\ +& \\ &~~68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:08 First, take two digits and add them.

00:11 Place the ones digit below, and carry over one to the tens.

00:15 Next, add the tens digits. Don't forget to include the one you carried over.

00:20 Write down the tens digit, and carry over one to the hundreds.

00:24 If there are missing digits, fill them with zero.

00:28 Add hundreds with hundreds, remember to add the one.

00:32 Place the hundreds digit below.

00:35 And that's how we solve the question! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &746 \\ +& \\ &~~68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers 746 and 68 by place value. Since 68 is a 2-digit number, place it beneath the 746 aligning to the right.
Step 2: Add the digits in the units place: 6 (from 746) + 8 (from 68) equals 14. Write down 4 and carry over 1 to the tens place.
Step 3: Add the digits in the tens place plus the carried over 1: 4 (from 746) + 6 (from 68) + 1 (carried over) equals 11. Write down 1 and carry over 1 to the hundreds place.
Step 4: Add the digits in the hundreds place plus any carry: 7 (from 746) + 0 (from 68 as there's no hundreds place in 68) + 1 (carried over) equals 8.

Thus, the complete sum is formed by reading down the digits you have written from top to bottom in each column after handling carries: 814.

Therefore, the solution to the problem is $814$ .

Final Answer

814

Key Points to Remember

Essential concepts to master this topic

Alignment: Place smaller number beneath larger, aligning right by place value
Technique: Add column by column: 6+8=14, write 4, carry 1
Check: Verify 746+68=814 by adding left to right: 700+40+6+60+8=814 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 14 in the units column when 6+8=14! This creates a wrong multi-digit result in one place. The 14 means you have 1 ten and 4 ones, so you must write 4 and carry the 1. Always carry any tens digit to the next column.

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

Why do I need to align the numbers to the right?

Place value alignment is crucial! The ones must line up with ones, tens with tens, etc. If you align left, you'd be adding hundreds to tens, which gives completely wrong results.

What does 'carry over' mean exactly?

When adding digits gives you 10 or more, the tens digit goes to the next column. Think of it like trading: 14 ones = 1 ten + 4 ones, so you carry that 1 ten to the tens place.

How do I add when one number is missing digits?

Treat missing digits as zero! In 746 + 68, there's no hundreds digit in 68, so it's really 746 + 068. Just add 7 + 0 + any carry for the hundreds place.

What if I forget to add the carried number?

You'll get the wrong answer! In this problem, forgetting the carried 1 in the tens place gives you 746 + 68 = 704 instead of 814. Always remember to add your carried digits.

Is there a way to check my answer without doing the problem again?

Yes! Use estimation: 746 + 68 is about 750 + 70 = 820. Your answer of 814 is close to 820, so it's reasonable. You can also try subtraction: 814 - 68 should equal 746.

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