# CLASS-4ADDITION - HORIZONTAL OR VERTICAL

Vertical addition is a method of adding two or more numbers that involves aligning them vertically and adding the digits in each column. Here are some properties of vertical addition:

1. Commutativity: The order in which the numbers are added does not affect the result. For example, 2 + 3 is the same as 3 + 2. Or Sum of the two numbers remains the same even if the order , in which they are added is changed. Example :- 384475 + 29580 = 414055. Also, 29580+ 384475 = 414055. Thus , 384475 + 29580 = 29580+ 384475
2. Associativity: The grouping of numbers being added does not affect the result. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). In what ever order three or more numbers are grouped for the purpose of addition, their sum remains the same .
3. Identity element: The number 0 is the identity element for addition, which means that adding 0 to any number does not change the value of the number. Addition of Zero – If ‘0’ is added to a number, we get the number itself.   Example:1)  892347 + 0 = 8923472.         Example.2) 3754093 + 0 = 3754093
4. Carrying: When adding two numbers vertically, carrying may be necessary when the sum of the digits in a column is greater than 9. This involves carrying the "tens" place digit over to the next column and adding it to the sum in that column.
5. Regrouping: If the sum of the digits in a column is greater than or equal to 10, regrouping may be necessary to correctly align the digits in the next column.
6. Place value: The position of a digit in a number indicates its place value, which is the value that the digit contributes to the overall value of the number. When adding numbers vertically, it is important to align digits according to their place values to ensure the correct result.

Example.1)             2    5    7    3     4

+   5    3    2    4     5

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7    8     9    7     9

Example.2)       8   2   7   9   4   3

3   4   9   4   5   6

+  5    3   8   7   3   7

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1  7    1   6   1   3   6