Commutative and associative law:

The commutative law for multiplication states in which numbers can be multiplied in any order, and the result is the similar product.  In equation form:

a x b = b x a

Therefore, the product of 8 x 3 is the similar as 3 x 8.

The associative law for multiplication states in which factors can be related in any order, and the result is the similar product.  In equation form:

a x (b x c) = (a x b) x c

Therefore, the numbers 2, 3, and 5 can be multiplied through first multiplying 2 x 3 to equal 6 and then multiplying 6 x 5 to equal 30.  The equation might also be solved through first multiplying 3 x 5 to equal 15, and after that multiplying 15 x 2 to equal 30.  In either case, a product is 30.

In multiplying two numbers, one number is placed under the other along with the digits arranged in columns placing units under the units place, tens under the tens place, and many more.  Commonly, the larger number is considered the multiplicand and the smaller number is considered the multiplier. A digit within the units place of the multiplier is multiplied first, the digit within the tens place of the multiplier additional, and many more.