Subtract multi-digit numbers

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Subtracting three-digit numbers involves a few more steps than simple subtraction, especially when you need to borrow from a higher place value. Understanding this process is crucial for accurate calculations. Here’s a detailed guide with examples:

Step-by-Step Guide:

  1. Align the Numbers: Write down the numbers vertically, aligning them by place value (hundreds, tens, and ones).
  2. Start from the Rightmost Column (Ones): Begin the subtraction from the ones place.
  3. Subtract Digit by Digit: Subtract the lower digit from the higher digit in each column, starting from the right.
  4. Borrow if Necessary: If the digit in the lower number is larger than the digit in the upper number in any column, you need to borrow from the next left column.
  5. Continue to the Left: Move to the tens column and then to the hundreds, repeating the process of subtraction and borrowing as necessary.

Examples:

  1. Simple Subtraction Without Borrowing
    • Example: 753 – 214
      • Subtract ones: 3 – 4 (cannot do, so borrow from the tens place)
      • After borrowing: 13 – 4 = 9
      • Subtract tens: 4 (originally 5, but we borrowed 1) – 1 = 3
      • Subtract hundreds: 7 – 2 = 5
      • Answer: 539
  2. Subtraction with Borrowing
    • Example: 605 – 157
      • Subtract ones: 5 – 7 (cannot do, so borrow from the tens place)
      • After borrowing: 15 – 7 = 8
      • Subtract tens: 0 (cannot borrow as it’s 0, so borrow from the hundreds place)
      • After borrowing, tens becomes 10: 10 – 5 = 5
      • Subtract hundreds: 5 (originally 6, but we borrowed 1) – 1 = 4
      • Answer: 448
  3. Subtracting Across Zeros
    • Example: 1000 – 123
      • Subtract ones: 0 – 3 (borrow from tens)
      • Borrow from tens, which is 0, so borrow from hundreds, which is also 0, finally borrow from thousands
      • After borrowing: 10 – 3 = 7
      • Tens becomes 10 after borrowing, then 10 – 2 = 8
      • Hundreds becomes 9 after borrowing, then 9 – 1 = 8
      • Subtract thousands: 0 (originally 1, but we borrowed 1) – 0 = 0
      • Answer: 877

Tips:

  • Borrowing: When borrowing, the digit to the left decreases by 1, and the current digit becomes 10 plus its original value.
  • Column by Column: Work your way from right to left, handling each column separately.
  • Line Up Your Numbers: Proper alignment is crucial for accurate subtraction.
  • Practice with Various Examples: Include examples with and without borrowing to build confidence.

Conclusion

Subtracting three-digit numbers, particularly with borrowing, is a foundational skill in arithmetic. It requires attention to the place value of each digit and understanding the concept of borrowing. With practice, this process becomes more intuitive and is a key skill for more advanced math problems. Remember to start from the right, borrow as needed, and work your way through each column methodically.

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