Solve Three-Digit Addition: 772 + 135 in Vertical Format

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

When adding digits in a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example, $7 + 3 = 10$ means write 0 and carry 1.

Q: Why do I need to line up the numbers vertically?

Place value alignment is crucial! The ones digits must be under ones digits, tens under tens, etc. This ensures you're adding the correct place values together.

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

Try these methods: Add the numbers in reverse order: $135 + 772$Use estimation: $800 + 100 = 900$, so 907 makes senseAdd each column again carefully

Q: Is there an easier way than carrying?

The carrying method is actually the most reliable way for multi-digit addition! While you might try mental math shortcuts, vertical addition with carrying ensures you don't miss any place values.

Column Addition with Carry-Over Operations

$\begin{aligned} &772 \\ +& \\ &135 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 calculate the sum of 2 digits, and then substitute

00:06 Let's start by adding ones with ones, and substitute in ones

00:09 Add tens with tens

00:13 Substitute tens in tens, add 1 to hundreds

00:17 Add hundreds with hundreds, remember to add 1 to the calculation

00:26 Substitute in hundreds

00:29 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

$\begin{aligned} &772 \\ +& \\ &135 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use a step-by-step vertical addition approach:

Step 1: Add the units place digits.

The units digit of $772$ is $2$ , and that of $135$ is $5$ . Adding these gives:

$2 + 5 = 7$

Step 2: Add the tens place digits, including any carry from the units place.

The tens digit of $772$ is $7$ , and that of $135$ is $3$ . Since there is no carry from the units place, we simply add the two digits:

$7 + 3 = 10$

We write down $0$ in the tens place and carry over $1$ to the hundreds place.

Step 3: Add the hundreds place digits, including any carry from the tens place.

The hundreds digit of $772$ is $7$ , and that of $135$ is $1$ . Including the carry of $1$ , we perform the addition:

$7 + 1 + 1 = 9$

Therefore, there is no additional carry to move forward.

Bringing all parts together, we form the resulting number. Hence, the sum is:

$907$

Final Answer

907

Key Points to Remember

Essential concepts to master this topic

Place Value: Always align digits in correct columns before adding
Carry Method: When tens place gives $7 + 3 = 10$ , write 0 carry 1
Verification: Check by adding in reverse order: $135 + 772 = 907$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't write down 10 in the tens place when $7 + 3 = 10$ = wrong answer 8017! This ignores place value rules and creates impossible digits. Always write the units digit (0) and carry the tens digit (1) 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

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

When adding digits in a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example, $7 + 3 = 10$ means write 0 and carry 1.

Why do I need to line up the numbers vertically?

Place value alignment is crucial! The ones digits must be under ones digits, tens under tens, etc. This ensures you're adding the correct place values together.

What if I forget to add the carried number?

You'll get the wrong answer! In this problem, forgetting to add the carried 1 in the hundreds place would give you $807$ instead of $907$ . Always double-check for carried numbers.

How can I check if my answer is correct?

Try these methods:

Add the numbers in reverse order: $135 + 772$
Use estimation: $800 + 100 = 900$ , so 907 makes sense
Add each column again carefully

Is there an easier way than carrying?

The carrying method is actually the most reliable way for multi-digit addition! While you might try mental math shortcuts, vertical addition with carrying ensures you don't miss any place values.

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