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How do you do long subtraction?

Published in Arithmetic 3 mins read

Long subtraction is a method used to subtract multi-digit numbers, especially when borrowing is required. It involves subtracting digits column by column, starting from the rightmost column (the ones place) and moving left. Here's a detailed explanation:

Steps for Long Subtraction:

  1. Write the numbers vertically: Align the numbers with the larger number (minuend) on top and the smaller number (subtrahend) below, making sure that the ones, tens, hundreds, and other place values are aligned in columns.

  2. Start subtracting from the rightmost column (ones place): Subtract the bottom digit from the top digit in the ones column.

    • If the top digit is greater than or equal to the bottom digit: Simply subtract and write the difference below the line in the ones place of your answer. For example, if you're subtracting 5 from 8, you get 3, so you write 3 in the ones place of the answer.

    • If the top digit is smaller than the bottom digit (borrowing is required): You need to borrow from the next column to the left (tens place).

      • Reduce the digit in the tens place by 1.
      • Add 10 to the digit in the ones place you're working with.
      • Now you can subtract. For example, if you need to subtract 7 from 3 in the ones place, you borrow 1 from the tens place, reducing the tens digit by 1. You add that "1" as a "10" to the 3 in the ones place, making it 13. Now you can subtract 7 from 13, which equals 6. Write 6 in the ones place of your answer.

  3. Move to the next column to the left (tens place): Repeat step 2 for the tens column, and then for the hundreds column, and so on, until you've subtracted all the columns. Remember to account for any borrowing you did in the previous steps.

  4. Write the result: The number written below the line is the difference between the two original numbers.

Example:

Let's subtract 357 from 824:

  824
- 357
------
  • Ones place: 4 - 7. Since 4 is smaller than 7, we need to borrow. Borrow 1 from the tens place (2 becomes 1). Add 10 to the ones place (4 becomes 14). Now, 14 - 7 = 7. Write 7 in the ones place of the answer.
  8 1(14)
- 3 5  7
------
      7
  • Tens place: Now we have 1 - 5. Since 1 is smaller than 5, we need to borrow again. Borrow 1 from the hundreds place (8 becomes 7). Add 10 to the tens place (1 becomes 11). Now, 11 - 5 = 6. Write 6 in the tens place of the answer.
  7(11)(14)
  8 2  4
- 3 5  7
------
     67
  • Hundreds place: Now we have 7 - 3 = 4. Write 4 in the hundreds place of the answer.
  7(11)(14)
  8 2  4
- 3 5  7
------
  4 67

Therefore, 824 - 357 = 467.

Key Points:

  • Always align the numbers correctly by place value.
  • Start subtracting from the rightmost column.
  • Borrow when the top digit is smaller than the bottom digit.
  • Keep track of borrowing.

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