Calculate the Sum: 285 + 11 in Vertical Format

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

Place value alignment ensures you're adding like values to like values - units to units, tens to tens, etc. Without proper alignment, you might accidentally add tens to hundreds!

Q: What do I do when there's no digit in a column?

When one number is shorter (like 11 vs 285), treat the missing digits as zeros. So 11 is really 011, making the hundreds place 2+0=2.

Q: Do I always start adding from the right side?

Yes, always start from the rightmost column! This follows the natural order of place values and helps you handle any carrying that might be needed in harder problems.

Q: How can I double-check my vertical addition?

Try adding the numbers horizontally: $ 285 + 11 = 296 $. If your vertical answer matches, you're correct! You can also use estimation: 285 + 11 should be close to 300.

Q: What if the numbers have different amounts of digits?

No problem! The shorter number just has implied zeros in the higher place values. Line up from the right, and the empty spaces on the left act like zeros.

Vertical Addition with Place Value Alignment

$\begin{aligned} &285 \\ +& \\ &~~11 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:02 Each time we calculate the sum of 2 digits, and then we substitute

00:05 Let's start by adding ones with ones

00:08 Substitute in ones place

00:12 Add tens with tens, substitute in tens place

00:15 Put 0 in the missing digits

00:19 Add hundreds with hundreds, substitute in hundreds place

00:23 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

$\begin{aligned} &285 \\ +& \\ &~~11 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem effectively, we will perform vertical addition as follows:

Step 1: Align the numbers 285 and 11 by place value:

$\begin{array}{c} ~~285 \\ +~~11 \\ \hline ~~? \\ \end{array}$

Step 2: Add the digits in each column, starting from the rightmost (units place):

- Units Place: $5 + 1 = 6$ . Write 6 in the units place.

- Tens Place: $8 + 1 = 9$ . Write 9 in the tens place.

- Hundreds Place: There’s no digit to add to 2 in this column, so it remains $2$ .

$\begin{array}{c} 285 \\ +11 \\ \hline 296 \\ \end{array}$

Step 3: Compile the result to get the final sum: 296.

Therefore, the solution to the problem is $296$ .

Final Answer

296

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with units column lined up
Technique: Add column by column from right to left: 5+1=6, 8+1=9
Check: Verify by adding horizontally: 285+11 should equal your vertical result ✓

Common Mistakes

Avoid these frequent errors

Misaligning place values when stacking numbers
Don't line up numbers by their left edges like 285 over 11 = wrong columns mixed up! This puts tens over hundreds and units over tens, giving completely wrong sums. Always align the rightmost digits (units place) first, then build left.

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

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

Place value alignment ensures you're adding like values to like values - units to units, tens to tens, etc. Without proper alignment, you might accidentally add tens to hundreds!

What do I do when there's no digit in a column?

When one number is shorter (like 11 vs 285), treat the missing digits as zeros. So 11 is really 011, making the hundreds place 2+0=2.

Do I always start adding from the right side?

Yes, always start from the rightmost column! This follows the natural order of place values and helps you handle any carrying that might be needed in harder problems.

How can I double-check my vertical addition?

Try adding the numbers horizontally: $285 + 11 = 296$ . If your vertical answer matches, you're correct! You can also use estimation: 285 + 11 should be close to 300.

What if the numbers have different amounts of digits?

No problem! The shorter number just has implied zeros in the higher place values. Line up from the right, and the empty spaces on the left act like zeros.

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