# multiplication

Multiplication and division are needed to solve many everyday problems. A man wants to tile the two main walls of a room [A], which is 5.5 meters long by 3 meters wide and 2 meters tall, using tiles 0.5 meters square. The walls can be drawn [B] as two areas of 22 square meters (m^{2}) and 12 m^{2}, giving a total area of 34 m^{2}. A single tile 0.5 m by 0.5 m has an area of 0.25 m^{2}. The number of tiles required [C] can be found by dividing the area of one tile (0.25 m^{2}). into the total area to be covered (34 m^{2}), giving the result 136 tiles. The same problem can be tackled another way [D]. If the whole area to be tiled is considered it measures 8.5 m by 4 m. The long side will accommodate 17 half-meter tiles and the short side only 8 tiles. The total number of tiles required is therefore 17 × 8 = 136, the same result as before but without calculating areas.

Multiplication is a way of combining two numbers to obtain a third; symbolized by ×,
., or merely the juxtaposition of the numbers (where suitable). Where *x* (the **multiplicand**) and *y* are natural
numbers, *x* × *y* is commutative and defined by *x* + *x* + ... + *x*, the number *x* appearing *y* times (see addition).

For multiplication of negative integers,
such as (-*x*) and (-*y*), (-*x*).*y* = *x*.(-*y*)
= -(*x*.*y*); and (-*x*).(*y*) = *x*.*y*.
Multiplication of any number by 0 (see zero)
is defined to give the product 0. Fractions may be multiplied by simple extension of the system. The inverse operation of multiplication is division,
since *x*/*y* = *x*.(1/*y*). In cases other
than with real numbers, multiplication
must be independently defined (see complex
number).

## product

A product is the result of one or more multiplications. Thus in *a.b = c*, the
product is *c*.