Addition and Subtraction - Subtraction of 5 and 6 digit numbers

Place Value Alignment: To subtract large numbers, write the $Minuend$ (larger number) above the $Subtrahend$ (smaller number). Align them vertically in a place value chart with columns for Lakhs ($L$), Ten-Thousands ($TTh$), Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). Imagine a vertical grid where each digit is perfectly stacked above its counterpart.

The Subtraction Terms: The number from which we subtract is the $Minuend$. The number being subtracted is the $Subtrahend$. The result obtained is called the $Difference$. This relationship is represented as $Minuend - Subtrahend = Difference$.

Subtraction without Regrouping: When every digit in the minuend is greater than or equal to the digit in the same place in the subtrahend, simply subtract each column starting from the right (Ones place). Visualise this as taking away a smaller group of items from a larger group in each specific column.

Subtraction with Regrouping (Borrowing): If a digit in the minuend is smaller than the digit in the subtrahend at the same place, we 'borrow' or regroup from the next higher place value. For example, borrowing $1$ Ten makes it $10$ Ones. In a written format, this is shown by crossing out the neighbor's digit, reducing it by $1$, and prefixing a '$1$' to the current digit.

Subtracting Across Zeros: When a number has zeros, you must regroup from the first non-zero digit to the left. For example, in the number $5,00,000$, to borrow for the Ones place, you must regroup from the Lakhs place, changing the intermediate zeros to $9$. Visualise this as a 'chain reaction' of borrowing across the place value columns.

Properties of Subtraction: Subtracting $0$ from any number results in the number itself ($x - 0 = x$). Subtracting a number from itself always results in zero ($x - x = 0$). These properties help in simplifying calculations involving multiple digits.

Inverse Relation for Checking: Subtraction is the inverse of addition. You can verify your answer by adding the $Difference$ to the $Subtrahend$. If the sum equals the $Minuend$, the calculation is correct. This can be visualised as 'rebuilding' the original number by putting the parts back together.