Solve Vertical Addition: Finding the Sum of 45 + 77

Column Addition with Two-Digit Carrying

45+77776 \begin{aligned} &45 \\ +& \\ &77 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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1

Understand the problem

45+77776 \begin{aligned} &45 \\ +& \\ &77 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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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, considering any carried value.
  • Step 3: Write down the resulting number as the answer.

Now, let's work through each step:
Step 1: Add the units digits. The units digit of 45 is 5, and the units digit of 77 is 7. Adding these gives: 5+7=12 5 + 7 = 12 . Since 12 is greater than 9, we write down 2 in the units column and carry over 1 to the tens column.
Step 2: Add the tens digits. The tens digit of 45 is 4, and the tens digit of 77 is 7. Including the carry-over 1 gives: 4+7+1=12 4 + 7 + 1 = 12 . Since 12 is a two-digit number, we write down 2 in the tens column and carry over 1 again, which is written in the hundreds column.
Step 3: Since there is nothing to add to the carried 1 in the hundreds column, we simply write it down as is.

Therefore, the solution to the problem is 122 122 .

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Final Answer

122

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always start adding from the rightmost column first
  • Technique: When sum exceeds 9, write units digit and carry tens: 5+7=12, write 2 carry 1
  • Check: Verify by adding horizontally: 45+77=122, same as column method ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't just write down 12 in the units column = wrong place value! When 5+7=12, you must write 2 in units and carry 1 to tens. Always carry the tens digit to the next column when sum is 10 or more.

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 'carry over' actually mean?

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When two digits add up to 10 or more, you write the units digit in that column and carry the tens digit to the next column. It's like breaking 12 12 into 10+2 10 + 2 !

Why can't I just write 12 in the units column?

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Because each column can only hold one digit! Writing 12 would mean you have 12 units, but 10 units equals 1 ten. So you write 2 units and carry the 1 ten to the tens column.

What if I need to carry more than once?

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That's totally normal! In this problem, we carried from units to tens (1), then from tens to hundreds (1). Just keep track of each carry-over as you work left.

How do I know if I carried correctly?

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Check your work by adding horizontally: 45+77=122 45 + 77 = 122 . If it matches your column answer, you carried correctly! Also, make sure each column shows only one digit.

What happens to the final carry-over?

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The final carry becomes a new digit in your answer! In this problem, the carry-over 1 becomes the hundreds digit, making our answer 122 instead of just 22.

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