Calculate the Sum: Adding 653 and 399 Using Place Value

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

Lining up by place value ensures you're adding ones to ones, tens to tens, and hundreds to hundreds. If numbers aren't aligned properly, you'll add the wrong digits together!

Q: What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example: 3+9=12, so write 2 and carry 1.

Q: Do I always start adding from the right?

Yes, always! Start from the rightmost column (ones place) and work left. This ensures you handle any carrying correctly as you move through each place value.

Q: What if I get confused with all the carrying?

Write small carry numbers above each column to keep track. For $653 + 399$, you'll have small 1's above the tens and hundreds places to remind you.

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

Try adding the numbers in reverse order (399 + 653) or use estimation: 653 is close to 650, 399 is close to 400, so 650 + 400 = 1050, which is close to 1052!

Column Addition with Carrying

$\begin{aligned} &653 \\ +& \\ &399 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 consider connecting 2 digits, and then we'll substitute

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

00:09 We'll place the units, add 1 to the tens

00:13 We'll add tens with tens, remember to add 1 to the calculation

00:16 We'll place tens in tens, add 1 to hundreds

00:21 We'll add hundreds with hundreds, remember to add 1

00:27 We'll place hundreds in hundreds, and add 1 to thousands

00:30 We'll place 0 in the missing digits

00:33 We'll add thousands with thousands, remember to add 1

00:36 We'll place in thousands

00:39 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

$\begin{aligned} &653 \\ +& \\ &399 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Line up the numbers according to their place values.
Step 2: Add the numbers column by column from right to left.
Step 3: Carry over any values greater than 9 to the next column.

Now, let's work through each step:

Step 1: Align the numbers vertically by place value:

$\begin{array}{c} \phantom{+}~~~~~653 \\ + \phantom{+}399 \\ \end{array}$

Step 2: Add the numbers in the ones column (rightmost column):

$3 + 9 = 12$

The result is 12. Place the 2 in the ones column and carry over 1 to the tens column.

Step 3: Add the numbers in the tens column, including the carry:

$5 + 9 + 1 = 15$

The result is 15. Place the 5 in the tens column and carry over 1 to the hundreds column.

Step 4: Add the numbers in the hundreds column, including the carry:

$6 + 3 + 1 = 10$

Place the 0 in the hundreds column and the 1 also in the next higher column (thousands place).

Therefore, the sum of $653$ and $399$ is $1052$ .

Final Answer

1052

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up numbers by place value before adding
Technique: Add right to left: 3+9=12, write 2, carry 1
Check: Count up from 653: 653+399 should equal 1052 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't just write down sums like 12 in the answer = wrong place values! When 3+9=12, you must write 2 in ones place and carry 1 to tens. Always carry the tens digit to the next column when your sum is 10 or more.

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 need to line up the numbers by place value?

Lining up by place value ensures you're adding ones to ones, tens to tens, and hundreds to hundreds. If numbers aren't aligned properly, you'll add the wrong digits together!

What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example: 3+9=12, so write 2 and carry 1.

Do I always start adding from the right?

Yes, always! Start from the rightmost column (ones place) and work left. This ensures you handle any carrying correctly as you move through each place value.

What if I get confused with all the carrying?

Write small carry numbers above each column to keep track. For $653 + 399$ , you'll have small 1's above the tens and hundreds places to remind you.

How can I check if my answer is right?

Try adding the numbers in reverse order (399 + 653) or use estimation: 653 is close to 650, 399 is close to 400, so 650 + 400 = 1050, which is close to 1052!

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