Solve Three-Digit Addition: 712 + 198 Step by Step

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

When you add digits and get 10 or more, you write the ones digit in that column and carry the tens digit to the next column on the left. Think of it like trading 10 ones for 1 ten!

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

We start from the ones place because any carrying affects the next column to the left. If we started from the left, we wouldn't know what to carry over!

Q: What if I forget to add the carried number?

Your answer will be too small! Always remember that carried numbers are part of the addition in that column. Double-check each column has all its numbers added together.

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

Try these methods: Add the numbers in reverse order (198 + 712)Use estimation: 700 + 200 = 900, so 910 makes senseAdd each column again carefully

Column Addition with Carrying Regrouping

$\begin{aligned} &712 \\ +& \\ &198 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem step by step.

00:07 First, we'll combine two digits at a time.

00:10 Let's begin by adding the ones place together.

00:14 After that, place the result and carry over any extra to the tens.

00:19 Now, add the tens place numbers, and don't forget to add the extra one.

00:25 Put the tens in the tens column and carry over one to the hundreds.

00:30 Next, add the hundreds together and remember to add one more.

00:36 Place the hundreds in the correct column.

00:40 And that's how we find the solution to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &712 \\ +& \\ &198 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Add the units digits: 2 (from 712) + 8 (from 198) = 10. Write down 0 and carry over 1 to the tens place.
Step 2: Add the tens digits and the carry: 1 (carry) + 1 (from 712) + 9 (from 198) = 11. Write down 1 and carry over 1 to the hundreds place.
Step 3: Add the hundreds digits and the carry: 1 (carry) + 7 (from 712) = 8 and 2 from 198 is not used here, we have already accounted it. Write down 9 as the total.

Thus, the final result of adding 712 and 198 is $910$ .

Final Answer

910

Key Points to Remember

Essential concepts to master this topic

Rule: Always start from the rightmost column (ones place)
Technique: When sum exceeds 9, write units digit and carry tens: 2+8=10, write 0 carry 1
Check: Add numbers in different order: 198+712 should equal 910 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over to the next column
Don't write down the full two-digit sum like 10 in the ones place = wrong place values! This ignores place value rules and creates impossible numbers. Always write the units digit and carry the tens digit 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 it mean to 'carry over' in addition?

When you add digits and get 10 or more, you write the ones digit in that column and carry the tens digit to the next column on the left. Think of it like trading 10 ones for 1 ten!

Why do I start adding from the right side?

We start from the ones place because any carrying affects the next column to the left. If we started from the left, we wouldn't know what to carry over!

What if I forget to add the carried number?

Your answer will be too small! Always remember that carried numbers are part of the addition in that column. Double-check each column has all its numbers added together.

How can I check if my addition is correct?

Try these methods:

Add the numbers in reverse order (198 + 712)
Use estimation: 700 + 200 = 900, so 910 makes sense
Add each column again carefully

What happens if I need to carry more than 1?

Sometimes you might carry 2 or even 3! For example, if a column adds up to 23, you write 3 and carry 2 to the next column. The same rule applies!

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