Solve 317 + 45: Vertical Format Addition Practice

Q: What does 'carry over' mean in addition?

When you add digits and get 10 or more, you can't write a two-digit number in one column. So you write the ones digit in that column and 'carry' the tens digit to the next column on the left.

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

Place value alignment ensures you're adding ones to ones, tens to tens, etc. If 45 isn't lined up properly under 317, you might accidentally add wrong digits together!

Q: What if one number has fewer digits than the other?

That's normal! Just imagine invisible zeros in the missing places. For example, 45 is really 045, so the hundreds place has 0 + 3 = 3.

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

Try these methods: Add in reverse order: 45 + 317 should give the same answerEstimate first: 300 + 50 ≈ 350, so 362 makes senseSubtract to check: 362 - 45 should equal 317

Q: What if I forget to carry a digit?

Your answer will be too small! For example, if you forget to carry the 1 from 7+5=12, you'd get 1+4=5 in tens place instead of 1+1+4=6. Always double-check your carrying.

Addition Algorithm with Carrying Digits

$\begin{aligned} &317 \\ +& \\ &~~45 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together!

00:08 We'll combine two digits at a time.

00:12 Start by adding the ones digits.

00:15 Write down the sum, and if needed, carry 1 to the tens.

00:19 Now add the tens digits. Don't forget to add that 1.

00:24 Place the result in the tens spot.

00:27 Don't forget to fill any missing digits with 0.

00:31 Next, add the hundreds digits and place the sum in the hundreds spot.

00:35 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &317 \\ +& \\ &~~45 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll carry out vertical addition:

Step 1: Add the rightmost digits (units place): $7 + 5 = 12$ . Since 12 is more than 9, we write 2 in the units place and carry over 1 to the tens place.
Step 2: Add the tens place along with the carried-over digit: $1 + 1 + 4 = 6$ . Write 6 in the tens place.
Step 3: Add the hundreds place: $3 + (0 \text{ since there is no hundreds digit from 45}) = 3$ . Write 3 in the hundreds place.

Therefore, the sum of the numbers 317 and 45 is $\mathbf{362}$ .

The correct choice from the given options that matches this sum is choice 4: $362$ .

Final Answer

362

Key Points to Remember

Essential concepts to master this topic

Place Value: Align digits by place value before starting vertical addition
Carrying: When sum ≥ 10, write units digit and carry tens to next column (7+5=12, write 2, carry 1)
Check: Verify by adding from left to right: 300+60+2=362 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry digits when sum exceeds 9
Don't just write 12 in the units place when 7+5=12! This ignores place value rules and creates impossible two-digit answers in single columns. Always write the units digit (2) and carry the tens digit (1) 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 'carry over' mean in addition?

When you add digits and get 10 or more, you can't write a two-digit number in one column. So you write the ones digit in that column and 'carry' the tens digit to the next column on the left.

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

Place value alignment ensures you're adding ones to ones, tens to tens, etc. If 45 isn't lined up properly under 317, you might accidentally add wrong digits together!

What if one number has fewer digits than the other?

That's normal! Just imagine invisible zeros in the missing places. For example, 45 is really 045, so the hundreds place has 0 + 3 = 3.

How can I check if my answer is correct?

Try these methods:

Add in reverse order: 45 + 317 should give the same answer
Estimate first: 300 + 50 ≈ 350, so 362 makes sense
Subtract to check: 362 - 45 should equal 317

What if I forget to carry a digit?

Your answer will be too small! For example, if you forget to carry the 1 from 7+5=12, you'd get 1+4=5 in tens place instead of 1+1+4=6. Always double-check your carrying.

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