Solve 728 + 182: Three-Digit Addition in Vertical Format

Three-Digit Addition with Carrying Operations

728+182776 \begin{aligned} &728 \\ +& \\ &182 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve the problem by combining numbers step-by-step.
00:10 Start by pairing two digits at a time. It helps keep things neat.
00:15 First, combine the ones digits. Ready?
00:19 Add the ones, and place them. Don't forget to carry one to the tens.
00:25 Now, focus on the tens digits. Add them up, plus the carried one.
00:30 Place the sum in the tens column, and carry one to the hundreds.
00:35 Next, add the hundreds digits, including the carried one.
00:40 Place the sum in the hundreds column.
00:43 Great job! That's how you solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

728+182776 \begin{aligned} &728 \\ +& \\ &182 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Align the numbers 728728 and 182182 vertically by their respective place values (ones, tens, hundreds).

  • Step 2: Add the digits in each column starting from the ones place and moving to the left (tens, then hundreds), carrying as necessary.

Now, let's work through each step:
Step 1: The numbers are aligned as follows:

728+182 \begin{array}{c} & 7 & 2 & 8 \\ + & 1 & 8 & 2 \\ \hline \end{array}

Step 2: Start adding from the rightmost column (ones):

8+2=108 + 2 = 10. We write down the 00 and carry over the 11 to the tens column.

Next, add the tens column including the carried 11:

2+8+1=112 + 8 + 1 = 11. We write down the 11 and carry over the 11 to the hundreds column.

Finally, add the hundreds column including the carried 11:

7+1+1=97 + 1 + 1 = 9. Write the 99.

Therefore, the sum is 910910.

The solution to the problem is 910\boxed{910}.

3

Final Answer

910

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value for accurate column addition
  • Technique: Start from ones column: 8 + 2 = 10, carry 1
  • Check: Verify by adding hundreds, tens, ones separately: 9 + 1 + 0 = 910 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when column sum exceeds 9
    Don't write 10 in the ones place when 8 + 2 = 10 = wrong answer 1010! The 1 represents ten ones which equals one ten. Always carry the 1 to the next column and write only the 0 in ones place.

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' in addition?

+

When a column adds up to 10 or more, you write the ones digit and carry the tens digit to the next column. For example, 8 + 2 = 10, so write 0 and carry 1.

Why do I start adding from the right side?

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We start from the ones place because any carrying affects the next column to the left. If you started from hundreds, you'd miss important carries from tens and ones!

What if I forget to add a carried number?

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Your answer will be too small! Always check each column carefully. In this problem, forgetting the carry gives 800 instead of 910 - a big difference!

How can I double-check my addition?

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Try these methods:

  • Add in reverse order (182 + 728)
  • Estimate first: 700 + 200 = 900, so 910 makes sense
  • Add each place value separately then combine

Is there a pattern to when I need to carry?

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Yes! You carry whenever the sum of a column is 10 or greater. In 728+182728 + 182, we carry from ones (8+2=10) and tens (2+8+1=11) but not hundreds (7+1+1=9).

What if there are more than two numbers to add vertically?

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The same rules apply! Add all numbers in each column, carry when the sum is 10 or more, and don't forget to include any carried amounts in your column totals.

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