Solve Vertical Subtraction: 2382 minus 453

Vertical Subtraction with Regrouping Steps

2382  453776 \begin{aligned} &2382 \\ -& \\ &~~453 \\ &\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 consider a shortage of 2 digits, and then we'll place
00:06 2 is less than 3
00:10 Therefore we subtract 1 from the tens, and add this amount to the ones
00:14 So now instead of 2 we will have 12
00:19 Subtract the ones from the ones plus the ten
00:23 Place in the ones
00:28 Subtract tens from tens, and place in tens
00:33 3 is less than 4
00:36 Therefore we subtract 1 from the thousands, and add this amount to the hundreds
00:41 So now instead of 3 we will have 13
00:44 Subtract the hundreds from the hundreds plus the hundred
00:50 Place in hundreds
00:54 Place 0 in the missing digits
00:57 Subtract thousands from thousands, and place in thousands
01:00 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

2382  453776 \begin{aligned} &2382 \\ -& \\ &~~453 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

Let's solve the problem using vertical subtraction with regrouping:

1. Start by aligning the numbers vertically by place value:

2382453 \begin{aligned} &2382 \\ - &\,453 \\ \end{aligned}

2. Perform subtraction starting from the units place (rightmost) column:

  • Units: 232 - 3. Since 22 is smaller than 33, we need to borrow from the tens place. Change 88 in the tens place to 77 and add 1010 to 22 to make it 1212. Now, 123=912 - 3 = 9.
  • Tens: Go to the tens column, which is now 757 - 5. Subtraction results in 22, as borrowing was resolved previously.
  • Hundreds: In the hundreds place, 343 - 4 is not possible without borrowing. Borrow from the thousands place: Change 22 to 11 (thousands place) and add 1010 to 33 (hundreds place), making it 1313. Now, 134=913 - 4 = 9.
  • Thousands: The thousands place subtraction is 101 - 0, which simply results in 11.

After completing the subtraction across each column, the final result is:

1929 \begin{aligned} &1929 \\ \end{aligned}

Thus, the solution to the subtraction problem is 19291929.

3

Final Answer

1929

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value before subtracting columns
  • Borrowing: When 2 - 3 is impossible, borrow 10 from next column
  • Verification: Add your answer 1929 + 453 = 2382 to check ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reduce the borrowed digit
    Don't borrow 10 from the tens place but leave it as 8 = wrong calculation! When you borrow, the 8 becomes 7, affecting the next column. Always reduce the digit you borrowed from by 1.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 3 from 2 in the ones place?

+

You can't subtract a larger number from a smaller one in subtraction! When 2 is smaller than 3, you need to borrow 10 from the tens place, making it 12 - 3 = 9.

How do I know when to borrow from the next column?

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Borrow whenever the top digit is smaller than the bottom digit in any column. Look at each column from right to left before starting your subtraction.

What happens to the digit I borrow from?

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The digit you borrow from gets reduced by 1. For example, when borrowing from the 8 in the tens place, it becomes 7. This is crucial for the next column's calculation!

Can I check my answer without adding?

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Yes! You can also estimate: 2382 - 453 should be close to 2400 - 450 = 1950. Since 1929 is close to 1950, your answer makes sense.

What if I need to borrow from a zero?

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When borrowing from 0, you need to borrow from the next non-zero digit to the left first. The 0 becomes 10, then you can borrow from it normally.

Why do we start subtracting from the right side?

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We start from the ones place (rightmost) because borrowing affects the column to the left. Working right to left ensures all borrowing is handled correctly.

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