and yields the result: Multiplication Multiplication is a mathematical operation that refers to the repetition of addition. When two numbers are multiplied together, the resulting value is called a product. The numbers being multiplied are called factors, with multiplicand and multiplier also used. For example, if there are five bags, each containing three apples, and the apples from all five bags are placed into an empty bag, the empty bag will contain 15 apples. This can be expressed as "five times three equals fifteen" or "five times three is fifteen" or "fifteen is the product of five and three". Multiplication can be thought of as a form of repeated addition, where the first factor indicates the number of times the second factor is added together. Multiplication is represented using the multiplication sign (×), as well as the asterisk (*) and parentheses (). Therefore, the statement "five times three equals fifteen" can be written as "5 × 3 = 15", "5 * 3 = 15", or "(5)(3) = 15". In some countries and in advanced arithmetic, other symbols may be used, such as the dot (⋅). In algebra, where numbers can be symbolized with letters, the multiplication symbol may be omitted; for example, xy represents x × y. The order in which two numbers are multiplied does not affect the result. This is known as the commutative property of multiplication. In the multiplication algorithm, the tens digit of the product of a pair of digits is referred to as the "carry digit". To multiply a pair of digits using a table, one must locate the intersection of the row of the first digit and the column of the second digit, which will contain the product of the two digits. Most pairs of digits result in two-digit numbers. Example of a multiplication algorithm for a single-digit factor Using the number 729 and 3, starting on the ones-column, the product of 9 and 3 are 27. 7 is written under the ones-column and 2 is written above the tens column as a carry digit. Next, the tens column. The product of 2 and 3 is 6, and the carry digit adds 2 to 6, so 8 is written under the tens column. Next, the hundreds-column. The product of 7 and 3 is 21, and since this is the last digit, 2 will not be written as a carry digit, but instead beside the