Addition

Addition of natural numbers is independent of the numerals used to represent the numbers being added. However, some forms of notation make addition of large numbers easier than other forms. In particular, the Hindu-Arabic positional notation (in general use today) facilitates addition of large numbers, while the use of Roman numerals, for instance, is quite cumbersome. In the Hindu-Arabic positional notation, numerals are arranged in columns, each column corresponding to numbers that are 10 times larger than those in the column to the immediate right. For example, 724 consists of 4 ones, 2 tens, and 7 hundreds. The addition algorithm amounts to counting by ones in the right hand column, counting by tens in the next column left, counting by hundreds in the next column left and so on. When the sum of two numbers in any column exceeds nine, the amount over 10 is retained and the rest transferred or "carried" to the next column left. Suppose it is desired to add 724 and 897. Adding each column gives 11 ones, 11 tens, and 15 hundreds. But 11 ones is equal to 1 ten and 1 one so we have 1 one, 12 tens and 15 hundreds. Checking the tens column we find 12 tens equals 2 tens and 1 hundred, so we actually have 1 one, 2 tens and 16 hundreds. Finally, 16 hundreds is 6 hundreds and 1 thousand, so the end result is 1 thousand, 6 hundreds, 2 tens, and 1 one, or 1,621.