Solve the Addition Problem: 276 + 54 in Vertical Format

Q: Why do I need to carry numbers when adding?

When a column sum is 10 or greater, you can't write a two-digit number in one place! Write the units digit and carry the tens digit to the next column left.

Q: How do I know where to place each number?

Use place value alignment: units column (ones), tens column, hundreds column. The smaller number 54 has no hundreds digit, so imagine a 0 there.

Q: How can I double-check my addition?

Use subtraction: 330 - 276 should equal 54, or 330 - 54 should equal 276. You can also add the numbers in reverse order as a verification!

Vertical Addition with Carrying Digits

$\begin{aligned} &276 \\ +& \\ &~~54 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 consider combining 2 digits, and then place

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

00:08 Write down the ones, add 1 to the tens

00:11 Add tens with tens, remember to add 1 to the calculation

00:16 Write down the tens in tens place, add 1 to hundreds

00:20 Write 0 in the missing digits

00:24 Add hundreds with hundreds remember to add 1, place in hundreds

00:30 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

$\begin{aligned} &276 \\ +& \\ &~~54 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll perform the following steps:

Align the numbers vertically with the smaller number (54) beneath the larger number (276), ensuring correct placement according to place values (units under units, tens under tens).
Add the units digits: $6 + 4 = 10$ . Write down 0 in the units place and carry over 1 to the tens place.
Add the tens digits: $7 + 5 = 12$ , plus the carried-over 1 gives us $13$ . Write down 3 in the tens place and carry over 1 to the hundreds place.
Add the hundreds digits: $2 + 0 = 2$ , plus the carried-over 1 gives us $3$ .

The numbers aligned look like this:

$\begin{aligned} & \phantom{1} 276 \\ + & \phantom{1} \underline{\phantom{0}54} \\ & \phantom{1} 330 \\ \end{aligned}$

Therefore, the solution to the problem is $330$ .

Final Answer

330

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Place digits in correct columns by place value
Technique: Add column by column: 6 + 4 = 10, write 0 carry 1
Check: Verify 330 - 54 = 276 matches original number ✓

Common Mistakes

Avoid these frequent errors

Misaligning numbers by place value
Don't line up numbers by their left edges like 276 above 54 = wrong column placement! This puts tens under hundreds and units under tens, giving incorrect sums. Always align numbers by place value with units under units, tens under tens.

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 carry numbers when adding?

When a column sum is 10 or greater, you can't write a two-digit number in one place! Write the units digit and carry the tens digit to the next column left.

What if I forget to add the carried number?

You'll get the wrong answer! In this problem, forgetting the carried 1 in the tens place would give you 320 instead of 330. Always remember to add any carried digits.

How do I know where to place each number?

Use place value alignment: units column (ones), tens column, hundreds column. The smaller number 54 has no hundreds digit, so imagine a 0 there.

Can I add from left to right instead?

It's much harder! Adding right to left (units first) is easier because you immediately know what to carry. Left to right requires mental math that's more error-prone.

What if both numbers have the same number of digits?

The process is identical! Just make sure each digit is properly aligned in its column. For example: $276 + 154$ would align perfectly in all three columns.

How can I double-check my addition?

Use subtraction: 330 - 276 should equal 54, or 330 - 54 should equal 276. You can also add the numbers in reverse order as a verification!

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