Solve Vertical Addition: 921 + 79 Step-by-Step

Vertical Addition with Three-Digit Carrying

921+  79776 \begin{aligned} &921 \\ +& \\ &~~79 \\ &\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
00:02 Each time consider combining 2 digits, and then place
00:05 Let's start by multiplying ones with ones
00:08 Place the ones, add 1 to tens
00:12 Multiply tens with tens, remember to add 1 to the calculation
00:18 Place tens in tens, add 1 to hundreds
00:21 Place 0 in the missing digits
00:24 Multiply hundreds with hundreds, remember to add 1
00:27 Place the hundreds in hundreds, add 1 to thousands
00:30 Place 0 in the missing digits
00:33 Multiply thousands with thousands, and place in thousands
00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

921+  79776 \begin{aligned} &921 \\ +& \\ &~~79 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Align the numbers vertically by place value.
  • Step 2: Add digits in each column starting from the right (units) to the left (hundreds), carrying over if necessary.
  • Step 3: Write the final sum at the bottom.

Let's work through the solution:

Step 1: We have the numbers aligned as:

921+  79 \begin{aligned} &921 \\ +& \\ &~~79 \\ \end{aligned}

Step 2: Start adding from the units column:

  • Units: 1+9=101 + 9 = 10. Write 0 and carry over 1 to the tens column.
  • Tens: 2+7+1 (carry over)=102 + 7 + 1 \text{ (carry over)} = 10. Write 0 and carry over 1 to the hundreds column.
  • Hundreds: 9+1 (carry over)=109 + 1 \text{ (carry over)} = 10. Write 0 and carry over 1 to a new thousands column.
  • Thousands: No additional digits to add, so just write 1.

Step 3: Combine the results to obtain the final sum:

The sum is 10001000.

Therefore, the solution to the problem is 1000 1000 .

3

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value before adding columns
  • Technique: Start right to left: 1+9=10, carry the 1
  • Check: Verify 921+79=1000 by adding horizontally: 900+21+79 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write down 10 in the ones column = wrong answer 99010! This happens when you forget that sums ≥10 need the tens digit carried to the next column. Always carry the tens digit and write only the ones digit in each column.

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' mean exactly?

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When adding digits gives you 10 or more, you write down the ones digit and 'carry' the tens digit to the next column. For example: 1+9=10 1 + 9 = 10 , so write 0 and carry 1.

Why do I start from the right side?

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You start from the ones place (rightmost) because carrying moves left to right - from smaller to larger place values. This ensures you handle all carries correctly!

What if I have more carries than expected?

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That's normal! In this problem, we carried three times and got a four-digit answer. Just keep carrying until you're done - the answer can have more digits than either original number.

How can I check my work without a calculator?

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  • Round and estimate: 921 + 79 ≈ 920 + 80 = 1000 ✓
  • Break apart: 921 + 79 = 921 + 80 - 1 = 1001 - 1 = 1000 ✓

What if the numbers aren't lined up properly?

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Always align by place value! The ones digits should be in the same column, tens digits aligned, etc. If 79 isn't right-aligned under 921, you'll get the wrong answer.

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