Solve Vertical Addition: 689 + 317 Step-by-Step

Q: What does 'carry' mean in addition?

When you add digits and get 10 or more, you write the ones digit below and carry the tens digit to the next column. For example: 9 + 7 = 16, so write 6 and carry the 1.

Q: Why do I start from the right side?

You start from the ones place (rightmost) because any carries need to go to the next higher place value. Working left to right would mess up your carrying!

Q: What if I get a carry in the last column?

If you carry from the highest place value (like hundreds), that carry becomes a new digit! In 689 + 317, the final carry of 1 becomes the thousands digit in 1006.

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

Try these methods: Add the columns again carefullyUse horizontal addition: $689 + 317 = 1006$Subtract one number from your answer to get the other

Q: What if I forget to carry a number?

Your answer will be too small! In this problem, forgetting carries gives 996 instead of 1006. Always double-check each column for carries ≥ 10.

Vertical Addition with Carry Operations

$\begin{aligned} &689 \\ +& \\ &317 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 connecting 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

00:12 Combine tens with tens, remember to add 1 to the calculation

00:17 Place tens in tens, add 1 to hundreds

00:21 Combine hundreds with hundreds, remember to add 1

00:25 Place hundreds in hundreds, and add 1 to thousands

00:31 Place 0 in the missing digits

00:34 Combine thousands with thousands, remember to add 1

00:38 Place in thousands

00:41 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

$\begin{aligned} &689 \\ +& \\ &317 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition starting from the rightmost digit:

Step 1: Add the units digits.
$9 + 7 = 16$ . Write down $6$ and carry over $1$ to the tens place.
Step 2: Add the tens digits.
$8 + 1 = 9$ , now add the carry $1$ , so $9 + 1 = 10$ . Write down $0$ and carry over $1$ to the hundreds place.
Step 3: Add the hundreds digits.
$6 + 3 = 9$ , now add the carry $1$ , so $9 + 1 = 10$ . Write down $0$ in the hundreds place and write down $1$ in the thousands place (since it's the final column, the carry becomes a leading digit).

Therefore, the sum of $689$ and $317$ is $\mathbf{1006}$ .

Final Answer

1006

Key Points to Remember

Essential concepts to master this topic

Rule: Start from rightmost column and work left systematically
Technique: When sum ≥ 10, write ones digit and carry tens digit: 9 + 7 = 16 → write 6, carry 1
Check: Add columns again or use horizontal addition: 689 + 317 = 1006 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add carried digits to next column
Don't just add 8 + 1 = 9 in tens place when you carried 1 from units! This gives 996 instead of 1006. Always remember to add the carried digit: 8 + 1 + 1(carry) = 10.

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 'carry' mean in addition?

When you add digits and get 10 or more, you write the ones digit below and carry the tens digit to the next column. For example: 9 + 7 = 16, so write 6 and carry the 1.

Why do I start from the right side?

You start from the ones place (rightmost) because any carries need to go to the next higher place value. Working left to right would mess up your carrying!

What if I get a carry in the last column?

If you carry from the highest place value (like hundreds), that carry becomes a new digit! In 689 + 317, the final carry of 1 becomes the thousands digit in 1006.

How can I check if my answer is right?

Try these methods:

Add the columns again carefully
Use horizontal addition: $689 + 317 = 1006$
Subtract one number from your answer to get the other

What if I forget to carry a number?

Your answer will be too small! In this problem, forgetting carries gives 996 instead of 1006. Always double-check each column for carries ≥ 10.

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