Subtraction - Subtraction of 4-digit Numbers with borrowing

Place Value Alignment: When subtracting 4-digit numbers, digits must be arranged in columns according to their place value: Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). Imagine a grid where each digit sits in its own box, perfectly aligned vertically with the digit it is being subtracted from.

Order of Subtraction: Always begin the subtraction process from the rightmost column, which is the Ones place, and then move progressively to the left through the Tens, Hundreds, and finally the Thousands column.

Minuend, Subtrahend, and Difference: The larger number at the top is called the Minuend, the number being subtracted is the Subtrahend, and the final result is known as the Difference. The relation is expressed as $Minuend - Subtrahend = Difference$.

Regrouping (Borrowing): If a digit in the minuend is smaller than the corresponding digit in the subtrahend, you must 'borrow' or regroup from the next higher place value to the left. For instance, if the Ones digit is too small, you borrow $1$ Ten from the Tens place.

Regrouping Hundreds and Thousands: Borrowing follows a base-10 pattern: $1$ Ten = $10$ Ones, $1$ Hundred = $10$ Tens, and $1$ Thousand = $10$ Hundreds. Visually, this is shown by crossing out the digit you are borrowing from, decreasing its value by $1$, and placing a small '$1$' in front of the digit that needs help.

Subtracting Across Zeros: If you need to borrow from a place value that contains a $0$, you must move further to the left (to the Hundreds or Thousands place) to find a non-zero digit. You regroup step-by-step from left to right until the required column has enough value to perform the subtraction.

Verification by Addition: You can check if your subtraction is correct by adding the Difference to the Subtrahend. If the sum equals the original Minuend, your answer is correct. This acts as a visual double-check for your work.