From Simple English Wikipedia, the free encyclopedia
Multiplication is anarithmetic operation for finding theproduct of twonumbers inmathematics, and is the opposite ofdivision. It is often represented by symbols such as or.[1][2] Multiplication is the third operation in math, after addition which is the first, and subtraction which is the second. It can also be defined on number mathematical objects as well.[3]
Withnatural numbers, multiplication gives the number of tiles in arectangle, where one of the two numbers equals the number of tiles on one side, and the other number equals the number of tiles on the other side.
Withreal numbers, multiplication gives thearea of arectangle where the first number is the same as the size of one side, and the second number is the same as the size of the other side.
For example, three multiplied by five is thetotal of five threesadded together, or the total of three fives. This can be written as 3 × 5 = 15, or spoken as "three times five equals fifteen."Mathematicians refer to the two numbers to be multiplied as "coefficients", or"multiplicand" and"multiplicator" separately (where multiplicand × multiplicator = product).
Multiplication between numbers is said to be commutative—when the order of the numbers does not influence the value of the product. This is true for theintegers (whole numbers), e.g. 4 × 6 is the same as 6 × 4, and also for therational numbers (fractions), and for all the otherreal numbers (representable as a field in the continuous line), and also forcomplex numbers (numbers representable as a field in the plane). However, it is not true forquaternions (numbers representable as a ring in the four-dimensional space),vectors ormatrices.
The definition of multiplication as repeated addition provides a way to arrive at a set-theoretic interpretation of multiplication of cardinal numbers. A more accurate representation is to think of it as scaling quantities. This animation illustrates 3 being multiplied by 2, giving 6 as a result. Notice that the blue dot in the blue segment of length 3 is placed at position 1, and the blue segment is scaled so that this dot is placed at the end of the red segment (of length 2). For multiplication by any X, the blue dot will always start at 1 and end at X. This works even if X is smaller than 1, or negative.
Teachers usually require their pupils to memorize the table of the first 9 numbers when teaching multiplication, so that more complex multiplication tasks can be performed.
