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
00:00 Solve
00:03 Each time we consider combining 2 digits, and then we'll write
00:06 Let's start by adding ones with ones
00:09 Write down the ones
00:12 Add tens with tens
00:15 Write down the tens in tens place, add 1 to hundreds
00:18 Write 0 in the missing digits
00:21 Add hundreds with hundreds, remember to add 1
00:25 Write down the hundreds in hundreds place, add 1 to thousands
00:28 Write 0 in the missing digits
00:31 Add thousands with thousands, and write in thousands
00:34 And this is the solution to the problem

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

\( \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

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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