Addition and Subtraction - Addition of 5 and 6 digit numbers

Place Value Alignment: When adding $5$-digit and $6$-digit numbers, always align the digits vertically according to their place values. Visualize a table with columns labeled Lakhs ($L$), Ten-Thousands ($TTh$), Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). Align the numbers from right to left to ensure the Ones place of each number is in the same column.

Addends and Sum: The individual numbers being added are called 'Addends,' and the total result obtained after addition is called the 'Sum.' In a column-style visual, the addends are placed one above the other, and the sum is written below a horizontal line.

Order of Operations: Addition always starts from the rightmost column (Ones place) and proceeds column by column to the left ($O \rightarrow T \rightarrow H \rightarrow Th \rightarrow TTh \rightarrow L$).

Regrouping (Carrying Over): If the sum of the digits in any column is $10$ or greater, you must regroup. Write the digit in the Ones place of that sum at the bottom of the column and 'carry over' the digit in the Tens place to the top of the next column on the left. Visually, these carry-overs are often written as small digits above the next place value column.

Order Property (Commutative): Changing the order of the addends does not change the sum. For example, $1,23,456 + 2,00,000$ will give the same result as $2,00,000 + 1,23,456$.

Grouping Property (Associative): When adding three or more numbers, the way you group the addends does not change the sum. This is helpful when adding three $5$-digit numbers mentally by grouping easy pairs first.

Identity Property of Zero: Adding $0$ to any $5$ or $6$-digit number results in the number itself. On a place value chart, a $0$ in a column means no value is added to that specific position.