Solve Three-Digit Addition: 137 + 523 in Vertical Format

Q: Why do I start adding from the right side instead of left?

We add from right to left because that's how our place value system works! Starting with ones, then tens, then hundreds ensures you handle carrying correctly.

Q: What does 'carrying over' actually mean?

Carrying over means when a column adds up to 10 or more, you write down the ones digit and add the tens digit to the next column. It's like exchanging 10 ones for 1 ten!

Q: How do I remember to carry the number over?

Write the carried number small and above the next column as a reminder. For example, when $7 + 3 = 10$, write a small 1 above the tens column.

Q: Can I add the numbers in a different order?

Yes! Addition is commutative, so $137 + 523$ gives the same result as $523 + 137$. But always align digits by place value!

Vertical Addition with Carrying Over

$\begin{aligned} &137 \\ +& \\ &523 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 calculate the sum of 2 digits, and then we substitute

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

00:13 We'll substitute the ones, add 1 to the tens

00:17 We'll add tens with tens, remember to add 1 to the calculation

00:28 We'll substitute in the tens place

00:34 We'll add hundreds with hundreds, substitute in the hundreds place

00:38 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

$\begin{aligned} &137 \\ +& \\ &523 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition of the numbers 137 and 523:

Step 1: Add the ones place: $7 + 3 = 10$ . We write down 0 and carry over the 1 to the tens place.
Step 2: Add the tens place: $3 + 2 = 5$ , and include the carried over 1, totaling $5 + 1 = 6$ . We write down 6.
Step 3: Add the hundreds place: $1 + 5 = 6$ . We write down 6.

By following these steps, the sum of the numbers 137 and 523 is calculated as 660.

Therefore, the solution to the problem is indeed $660$ , which matches with choice 2 among the given options.

Final Answer

660

Key Points to Remember

Essential concepts to master this topic

Rule: Always add column by column from right to left
Technique: When sum exceeds 9, write ones digit and carry tens digit: $7 + 3 = 10$ → write 0, carry 1
Check: Verify by adding horizontally: $137 + 523 = 660$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when column sum is 10 or more
Don't write down the full two-digit sum like writing 10 in the ones place = wrong answer like 6510! This ignores place value completely. Always write only the ones digit and carry the tens digit 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 start adding from the right side instead of left?

We add from right to left because that's how our place value system works! Starting with ones, then tens, then hundreds ensures you handle carrying correctly.

What does 'carrying over' actually mean?

Carrying over means when a column adds up to 10 or more, you write down the ones digit and add the tens digit to the next column. It's like exchanging 10 ones for 1 ten!

How do I remember to carry the number over?

Write the carried number small and above the next column as a reminder. For example, when $7 + 3 = 10$ , write a small 1 above the tens column.

What if I forget to add the carried number?

Your answer will be wrong! Always check each column carefully. In this problem, forgetting the carried 1 would give you 650 instead of the correct answer 660.

Can I add the numbers in a different order?

Yes! Addition is commutative, so $137 + 523$ gives the same result as $523 + 137$ . But always align digits by place value!

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