Solve Three-Digit Addition: 877 + 656 in Vertical Format

Q: What does 'carrying' mean in addition?

When a column adds up to 10 or more, you write down the units digit and carry the tens digit to the next column. For example, $7 + 6 = 13$ means write 3 and carry 1.

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

Proper alignment ensures you're adding units to units, tens to tens, and hundreds to hundreds. Misalignment leads to completely wrong answers!

Q: What if I forget to add the carried number?

Always remember to add your carried number to the next column! Write it small above the column as a reminder. Forgetting it gives you an answer that's too small.

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

Try these methods: Add the numbers in reverse orderUse estimation: $900 + 700 = 1600$ (close to 1533)Add each column again carefully

Q: What if I get confused with multiple carries?

Take it one column at a time! Write down each carried number clearly above the next column. Don't rush - accuracy is more important than speed.

Column Addition with Carrying Operations

$\begin{aligned} &877 \\ +& \\ &656 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 we consider combining 2 digits, and then we'll place

00:06 Let's start by combining ones with ones

00:09 Place the ones, add 1 to the tens

00:16 Combine tens with tens, remember to add 1 to the calculation

00:24 Place tens in tens, add 1 to hundreds

00:30 Combine hundreds with hundreds, remember to add 1

00:35 Place hundreds in hundreds, and add 1 to thousands

00:39 Place 0 in the missing digits

00:42 Combine thousands with thousands, remember to add 1

00:45 Place in thousands

00:48 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &877 \\ +& \\ &656 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform the addition of the numbers 877 and 656 using the vertical column method. Let's break it down step by step:

Step 1: Write the numbers vertically aligned by their place values: units, tens, and hundreds.
Step 2: Start by adding the units column (rightmost column): $7 + 6 = 13$ . Write down 3 in the units place and carry over 1 to the tens place.
Step 3: Next, add the tens column: $7 + 5 = 12$ . Adding the carryover 1 gives total $13$ . Write down 3 in the tens place and carry over 1 to the hundreds place.
Step 4: Finally, add the hundreds column: $8 + 6 = 14$ . Adding the carryover 1 gives total $15$ . Since this is the leftmost column, write down the entire result, 15, in the appropriate place.

The sum of the numbers is therefore $1533$ .

Hence, the correct answer to the problem is $1533$ .

Final Answer

1533

Key Points to Remember

Essential concepts to master this topic

Rule: Align digits by place value and add column by column
Technique: When sum exceeds 9, write units digit and carry tens: $7 + 6 = 13$ → write 3, carry 1
Check: Verify by adding in reverse order: $656 + 877 = 1533$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't write 13 directly in one column = wrong place values! This creates numbers like 131313 instead of the correct answer. Always write only the units digit and carry the 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

What does 'carrying' mean in addition?

When a column adds up to 10 or more, you write down the units digit and carry the tens digit to the next column. For example, $7 + 6 = 13$ means write 3 and carry 1.

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

Proper alignment ensures you're adding units to units, tens to tens, and hundreds to hundreds. Misalignment leads to completely wrong answers!

What if I forget to add the carried number?

Always remember to add your carried number to the next column! Write it small above the column as a reminder. Forgetting it gives you an answer that's too small.

How can I check if my addition is correct?

Try these methods:

Add the numbers in reverse order
Use estimation: $900 + 700 = 1600$ (close to 1533)
Add each column again carefully

What if I get confused with multiple carries?

Take it one column at a time! Write down each carried number clearly above the next column. Don't rush - accuracy is more important than speed.

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