Solve Vertical Addition: 45 + 5 Step-by-Step

Vertical Addition with Carrying Over

45+  5776 \begin{aligned} &45 \\ +& \\ &~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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1

Understand the problem

45+  5776 \begin{aligned} &45 \\ +& \\ &~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Add the ones place digits.
  • Step 2: If needed, adjust by carrying over any excess to the tens place.
  • Step 3: Add the tens place digits.

Now, let's work through each step:
Step 1: We start by adding the digits in the ones place: 5+5=105 + 5 = 10. Since 1010 is greater than 99, we write down 00 in the ones place and carry over 11 to the tens place.
Step 2: Then, add the tens place digits. The tens digit of 45 is 4, and we add the carried over 1: 4+1=54 + 1 = 5.
Step 3: Therefore, after adding, the complete sum is 5050.

Thus, the solution to the problem is 50 50 , which corresponds to choice 4.

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Always align digits by ones, tens, hundreds columns
  • Carrying Technique: When sum ≥ 10, write remainder and carry 1 left
  • Check: Count up from larger number: 45 + 5 = 50 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when ones place sum equals 10 or more
    Don't just write 10 in the ones place = 4510 instead of 50! When 5 + 5 = 10, you must write 0 in ones place and carry 1 to tens place. Always carry over when the sum is 10 or greater.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why do I need to carry over when I get 10?

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Because 10 has two digits but the ones place can only hold one digit! The 0 stays in ones place, and the 1 moves to the tens place to show the correct value.

What if I forget to carry over?

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You'll get the wrong answer! For example, 5 + 5 = 10, but if you don't carry, you might write 410 instead of the correct answer 50.

How do I remember which direction to carry?

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Always carry to the left! Think of it like filling up containers - when the ones place is full (10), the extra goes to the bigger container (tens place).

Can I check my answer a different way?

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Yes! Try counting up from the larger number: start at 45, then count 5 more: 46, 47, 48, 49, 50. You should get the same answer!

What happens if both numbers have the same digits in ones place?

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Like this problem where both end in 5! You'll often need to carry because 5 + 5 = 10, 7 + 7 = 14, etc. Just remember the carrying rule.

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