Products and quotients are the results obtained by applying the operations of multiplication and division, respectively, to particular mathematical objects. Both will be examined; products first, followed by quotients.

Product is defined in mathematics as the quantity obtained by multiplying one quantity or expression by another quantity or expression. For instance, the expression "5 x 6" is the product of the whole numbers "5" and "6". Products are encountered in elementary arithmetic: children typically learn by rote the products of various whole numbers. Beyond whole numbers, there are also products of integers, rational numbers, real numbers, and complex numbers, as well as products of vectors, functions, matrices, tensors, and other 'higher' mathematical objects.

The word product first appeared in use during the first half of the 15th century. Product is from the Middle English and the Medieval Latin word "productum" (something produced), which was derived from the neuter...