Solve Vertical Addition: 954 + 72 Step-by-Step

Vertical Addition with Three-Digit Numbers

954+  72776 \begin{aligned} &954 \\ +& \\ &~~72 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together!
00:08 First, we'll combine two digits at a time.
00:11 Start by adding the ones digits.
00:14 Write down the result in the ones place.
00:17 Next, add the tens digits.
00:20 Place the sum in the tens space and add one to the hundreds.
00:24 Fill any missing spaces with zero.
00:27 Add the hundreds digits and remember to add one!
00:31 Write the result in the hundreds place and one more to the thousands.
00:36 Again, fill any blanks with zero.
00:40 Add the thousands digits and record it in the thousands space.
00:44 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

954+  72776 \begin{aligned} &954 \\ +& \\ &~~72 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Start with the units' column addition.
  • Step 2: Add the tens' column, accounting for any carryover from the units' column.
  • Step 3: Add the hundreds' column, accounting for any carryover from the tens' column.

Now, let's work through each step:

Step 1: Add the units' place:
The units' place in 954 is 4, and in 72, it is 2. Add these together: 4+2=6 4 + 2 = 6 .
Place 6 in the units' position of our result.

Step 2: Add the tens' place:
The tens' place in 954 is 5, and in 72, it is 7. Add these together: 5+7=12 5 + 7 = 12 .
Since 12 is greater than 9, place 2 in the tens' position and carry over 1 to the hundreds' column.

Step 3: Add the hundreds' place:
The hundreds' place in 954 is 9. Add the carry over 1 from the tens' addition: 9+1=10 9 + 1 = 10 .
This gives us 0 in the hundreds' position, with another carry over 1 to the next column which becomes a thousand.
This forms 1 in the thousand's position of our result.

Therefore, the sum of 954 and 72 is 1026 1026 .

Among the provided choices, choice 4 corresponds to this solution.

3

Final Answer

1026

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Align digits by place value in vertical columns
  • Carrying: When sum ≥ 10, write ones digit and carry tens digit left
  • Verification: Check by adding in reverse order: 72 + 954 = 1026 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when column sum exceeds 9
    Don't write 12 in the tens column when 5 + 7 = 12! This creates an invalid two-digit result in one place value position. Always write the ones digit (2) and carry the tens digit (1) to the next column left.

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 over' a number?

+

When adding digits in a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column left. For example, 5 + 7 = 12, so write 2 and carry the 1.

Why do I need to line up the numbers vertically?

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Place value alignment is crucial! The ones digits must be in the same column, tens digits in the same column, etc. This ensures you're adding the correct place values together.

What if one number has fewer digits than the other?

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That's normal! In 954 + 72, there's no hundreds digit in 72, so treat it as 0. Just add 9 + 0 = 9 in the hundreds column (plus any carry-over).

How can I check if my answer is correct?

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Try these methods:

  • Reverse addition: Add 72 + 954 instead
  • Estimation: 950 + 70 = 1020, close to 1026 ✓
  • Subtraction check: 1026 - 72 should equal 954

What if I get confused about which direction to carry?

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Always carry to the left! Remember: place values get bigger as you move left (ones → tens → hundreds → thousands). The carried digit represents a higher place value.

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