Elementary Arithmetic - Multiplication

Multiplication

When two numbers are multiplied together, the result is called a product. The two numbers being multiplied together are called factors.

What does it mean to multiply two natural numbers? Suppose there are five red bags, each one containing three apples. Now grabbing an empty green bag, move all the apples from all five red bags into the green bag. Now the green bag will have fifteen apples. Thus the product of five and three is fifteen. This can also be stated as "five times three is fifteen" or "five times three equals fifteen" or "fifteen is the product of five and three". Multiplication can be seen to be a form of repeated addition: the first factor indicates how many times the second factor should be added onto itself; the final sum being the product.

Symbolically, multiplication is represented by the multiplication sign: ×. So the statement "five times three equals fifteen" can be written symbolically as

In some countries, and in more advanced arithmetic, other multiplication signs are used, e.g. 5 ⋅ 3. In some situations, especially in algebra, where numbers can be symbolized with letters, the multiplication symbol may be omitted; e.g. xy means x × y. The order in which two numbers are multiplied does not matter, so that, for example, three times four equals four times three. This is the commutative property of multiplication.

To multiply a pair of digits using the table, find the intersection of the row of the first digit with the column of the second digit: the row and the column intersect at a square containing the product of the two digits. Most pairs of digits produce two-digit numbers. In the multiplication algorithm the tens-digit of the product of a pair of digits is called the "carry digit".