Solve Vertical Addition: 597 + 65 Using Column Method

Q: What does 'carrying' actually mean in addition?

Carrying happens when a column sum is 10 or more. The extra amount (tens digit) gets carried over to the next column because it represents the next place value. For example, 7+5=12 means 1 ten and 2 ones.

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

Each column represents a different place value - units, tens, hundreds. If you don't align properly, you might add tens to units or hundreds to tens, giving you a completely wrong answer!

Q: What if I forget to carry a number?

Your final answer will be too small! For example, forgetting to carry 1 in this problem would give you 652 instead of 662. Always double-check that you've added any carried numbers.

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

Try these methods: Add in reverse order (65+597)Estimate first (600+70=670, close to 662)Use subtraction to verify (662-65=597)

Column Addition with Three-Digit Carrying

$\begin{aligned} &597 \\ +& \\ &~~65 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem.

00:08 Each time, we'll combine two digits. Let's go!

00:12 We'll start by combining the ones with the ones.

00:15 Place the ones value, then add one to the tens.

00:19 Now, combine the tens with the tens. Remember to add one when adding.

00:24 Place the tens value, then add one to the hundreds.

00:29 Fill any missing digit spaces with zero.

00:33 Lastly, combine the hundreds with hundreds. Don't forget to add one!

00:37 That's the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &597 \\ +& \\ &~~65 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll add the numbers 597 and 65 using vertical addition.

Write the numbers vertically, aligning them by their place values (units, tens, hundreds):

597
+ 65

Step 1: Add the units column:

Add 7 (from 597) and 5 (from 65) to get 12. Write 2 in the units column and carry over 1 to the tens column.

Step 2: Add the tens column:

Add 9 (from 597), 6 (from 65), and the carried over 1 to get 16. Write 6 in the tens column and carry over 1 to the hundreds column.

Step 3: Add the hundreds column:

Add 5 (from 597) and the carried over 1 to get 6. Write 6 in the hundreds column.

Therefore, the sum of 597 and 65 is $662$ .

Final Answer

662

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value columns (units, tens, hundreds)
Carrying: Write units digit, carry tens: 7+5=12, write 2, carry 1
Verification: Check each column calculation and final sum: 597+65=662 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add carried numbers to the next column
Don't ignore the carried 1 when adding the tens column = wrong total like 652! The carried number represents ten units that must be included. Always add the carried digit to your next column calculation.

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

What does 'carrying' actually mean in addition?

Carrying happens when a column sum is 10 or more. The extra amount (tens digit) gets carried over to the next column because it represents the next place value. For example, 7+5=12 means 1 ten and 2 ones.

Why do I need to line up the numbers by columns?

Each column represents a different place value - units, tens, hundreds. If you don't align properly, you might add tens to units or hundreds to tens, giving you a completely wrong answer!

What if I forget to carry a number?

Your final answer will be too small! For example, forgetting to carry 1 in this problem would give you 652 instead of 662. Always double-check that you've added any carried numbers.

How can I check if my addition is correct?

Try these methods:

Add in reverse order (65+597)
Estimate first (600+70=670, close to 662)
Use subtraction to verify (662-65=597)

What if there's nothing to add in the hundreds column?

Since 65 has no hundreds digit, you only add the hundreds digit from 597 (which is 5) plus any carried amount. In this case: 5+1=6 in the hundreds place.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime