Solve Three-Digit Addition: 156 + 254 Using Vertical Format

Vertical Addition with Carrying

156+254776 \begin{aligned} &156 \\ +& \\ &254 \\ &\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 combining 2 digits, and then place
00:06 Let's start by combining ones with ones
00:09 Place the ones, add 1 to the tens
00:12 Combine tens with tens, remember to add 1 to the calculation
00:20 Place tens in tens, add 1 to hundreds
00:24 Combine hundreds with hundreds, remember to add 1
00:30 Place in hundreds
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

156+254776 \begin{aligned} &156 \\ +& \\ &254 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Add the digits in the units column.
  • Step 2: Add the digits in the tens column, including any carry from the units column.
  • Step 3: Add the digits in the hundreds column, including any carry from the tens column.

Now, let's work through each step:

Step 1: Adding Units
- Consider the rightmost column (units place). We add the digits: 66 (from 156) and 44 (from 254).
- 6+4=106 + 4 = 10.
- We write down 00 in the units place and carry over 11 to the tens place.

Step 2: Adding Tens
- Move to the next column on the left (tens place). We add the digits: 55 (from 156), 55 (from 254), plus the carry-over 11 from the previous step.
- 5+5+1=115 + 5 + 1 = 11.
- We write down 11 in the tens place and carry over 11 to the hundreds place.

Step 3: Adding Hundreds
- Move to the hundreds column. We add the digits: 11 (from 156), 22 (from 254), plus the carry-over 11.
- 1+2+1=41 + 2 + 1 = 4.
- We write down 44 in the hundreds place.

Putting it all together, the sum of 156+254=410156 + 254 = 410.

Therefore, the solution to the problem is 410 410 .

3

Final Answer

410

Key Points to Remember

Essential concepts to master this topic
  • Column Rule: Start from the rightmost column and work left
  • Carrying: When sum equals 10 or more, write ones digit and carry tens
  • Check: Add numbers horizontally: 156 + 254 = 410 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add the carried digit
    Don't add 5 + 5 = 10 in the tens column without including the carried 1 = wrong answer of 400! This ignores the regrouping from the units column. Always add the carried digit to get 5 + 5 + 1 = 11.

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 carry when adding?

+

Carrying happens when the sum in a column is 10 or more. Since each place value can only hold digits 0-9, we write the ones digit and carry the tens digit to the next column left.

What if I forget to carry a number?

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Your final answer will be too small! For example, if you forget the carry in this problem, you'd get 400 instead of 410. Always double-check each column for carries.

Can I add the numbers in any order?

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Yes! Addition is commutative, meaning 156+254 156 + 254 gives the same result as 254+156 254 + 156 . The vertical format just makes carrying easier to track.

How do I check if my answer is correct?

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Try adding horizontally: 156+254 156 + 254 . You can also estimate by rounding: 160+250=410 160 + 250 = 410 , which matches our exact answer!

What if there are more carries in harder problems?

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Same process! Just work column by column from right to left. Sometimes you might carry multiple times, but the steps stay the same: add the digits plus any carry, then carry again if needed.

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