Solve Vertical Addition: 522 + 87 Step-by-Step

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

Lining up by place value ensures you add ones to ones, tens to tens, and hundreds to hundreds. If numbers aren't aligned properly, you'll get the wrong answer!

Q: What happens when I add 2 + 8 in the tens column?

Since $ 2 + 8 = 10 $, you write 0 in the tens place and carry the 1 to the hundreds column. This 1 represents 1 hundred, not just 1!

Q: How do I know when to carry over?

Carry over whenever the sum in any column is 10 or greater. Write the ones digit of that sum and carry the tens digit to the next column.

Q: How can I check if my answer 609 is correct?

Try different methods: Add horizontally: $ 500 + 80 + 22 + 7 = 609 $Use subtraction: $ 609 - 87 = 522 $ ✓Estimate: $ 520 + 90 ≈ 610 $ (close!)

Vertical Addition with Carrying Hundreds

$\begin{aligned} &522 \\ +& \\ &~~87 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:02 Each time consider joining 2 digits, and then we'll write

00:05 Let's start by adding ones with ones

00:08 Write down the ones

00:11 Add tens with tens

00:14 Write down tens in tens, add 1 to hundreds

00:17 Write 0 in the missing digits

00:20 Add hundreds with hundreds remember to add 1, write in hundreds

00:24 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

$\begin{aligned} &522 \\ +& \\ &~~87 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Identify the digits and add them from right to left.
Step 2: Handle any carry-over between columns.
Step 3: Record the final result.

Now, let's work through the addition:

Step 1: Add the ones digits: $2 + 7 = 9$ . Place $9$ in the ones place of the result.
Step 2: Add the tens digits: $2 + 8 = 10$ . Place $0$ in the tens place, and carry over $1$ to the hundreds place.
Step 3: Add the hundreds digit: $5 + 1 = 6$ (including the carry-over). Place $6$ in the hundreds place of the result.

Thus, the sum $522 + 87$ is $609$ .

Therefore, the solution to the problem is $609$ .

Final Answer

609

Key Points to Remember

Essential concepts to master this topic

Rule: Add columns from right to left, handling carries properly
Technique: When tens sum exceeds 9, write remainder and carry 1
Check: Verify $522 + 87 = 609$ by adding horizontally ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum exceeds 9
Don't write 10 in the tens place when 2 + 8 = 10! This ignores place value rules and gives 52210 instead of 609. Always write the ones digit (0) and carry the tens digit (1) 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

Why do I need to line up the numbers by place value?

Lining up by place value ensures you add ones to ones, tens to tens, and hundreds to hundreds. If numbers aren't aligned properly, you'll get the wrong answer!

What happens when I add 2 + 8 in the tens column?

Since $2 + 8 = 10$ , you write 0 in the tens place and carry the 1 to the hundreds column. This 1 represents 1 hundred, not just 1!

How do I know when to carry over?

Carry over whenever the sum in any column is 10 or greater. Write the ones digit of that sum and carry the tens digit to the next column.

Can I add from left to right instead?

It's much harder! Adding right to left lets you handle carries as you go. If you go left to right, you might need to go back and fix previous columns when carries occur.

How can I check if my answer 609 is correct?

Try different methods:

Add horizontally: $500 + 80 + 22 + 7 = 609$
Use subtraction: $609 - 87 = 522$ ✓
Estimate: $520 + 90 ≈ 610$ (close!)

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