In mathematics, multiplication is an elementary arithmetic operation. When one of the numbers is a whole number, multiplication is the repeated sum of the other number.
For example, 7 × 4 is the same as 7 + 7 + 7 + 7.
A multiplication chart (times table or multiplication table, as used to teach schoolchildren multiplication) is a grid where rows and columns are headed by the numbers to multiply, and the entry in each cell is the product of the column and row headings.
So, for example, 3×6=18 by looking up where 3 and 6 intersect. This chart does not give the zeros. That is because any real number times zero is zero. Multiplication tables vary from country to country. They may have ranges from 1×1 to 10×10, from 2×1 to 9×9, or from 1×1 to 12×12 to quote a few examples.
Multiplication chart 1-12
The traditional rote learning of multiplication was based on memorisation of columns in the chart, in a form like:
1 × 7 = 7
2 × 7 = 14
3 × 7 = 21
4 × 7 = 28
5 × 7 = 35
6 × 7 = 42
7 × 7 = 49
8 × 7 = 56
9 × 7 = 63
Multiplication can be defined for real and complex numbers, polynomials, matrices and other mathematical quantities as well. The inverse of multiplication is division.
Multiplication chart 1-20
Fractions are multiplied by separately multiplying their denominators and numerators: a/b × c/d = (ac)/(bd). For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
Binary operation
In mathematics, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division.
Notation and terminology
Multiplication is often written using the multiplication sign "×" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,
2 x 3 = 6 (verbally, "two times three equals six")
3 x 4 = 12
2 x 3 x 5 = 6 x 5 = 30
2 x 2 x 2 x 2 x 2 = 32
There are several other common notations for multiplication. Many of these are to reduce confusion between the multiplication sign × and the commonly-used variable x:
Multiplication is sometimes denoted by either a middle dot or a period:
5 . 2
The middle dot is standard in the United States, the United Kingdom, and other countries where the period is used as a decimal point. In other countries that use a comma as a decimal point, either the period or a middle dot is used for multiplication.
The asterisk (as in 5*2) is often used in programming languages because it appears on every keyboard. This usage originated in the FORTRAN programming language.
In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).
In matrix multiplication, there is actually a distinction between the cross and the dot symbols. The cross symbol generally denotes a vector multiplication, while the dot denotes a scalar multiplication. A like convention distinguishes between the cross product and the dot product of two vectors.
The numbers to be multiplied are generally called the "factors" or "multiplicands". When thinking of multiplication as repeated addition, the number to be multiplied is called the "multiplicand", while the number of multiples is called the "multiplier". In algebra, a number that is the multiplier of a variable or expression (e.g. the 3 in 3xy2) is called a coefficient.
The result of a multiplication is called a product, and is a multiple of each factor that is an integer. For example 15 is the product of 3 and 5, and is both a multiple of 3 and a multiple of 5.
Chart
A chart or graph is a type of information graphic, that represents tabular numeric data and/or functions. Charts are often used to make large quantities of data more easily understandable, and recognizable on first view.
Charts can represent data in several different ways. Some of the different methods are listed below. Charts represent data in different ways depending on the type of data that is presented. For example, a customer satisfaction response may be measured in percentages - the percentage of customers satisfied, not satisfied, and unsure. In this instance, a "pie chart" may be used successfully. A pie chart is visually appealing and allows for greatest recognition since the number of satisfaction responses can be easily compared to the number of dissatisfaction responses by comparing the size of each sector of the pie graph, which is not easily done if presented, for example, in a histogram (or bar chart).
Charts can be created dynamically by computers using a charting application.
Charts are not always used for mathematical purposes, but are also used in many widely differing areas.
Examples of various charts:
Statistics
Bar chart
Pie chart
Histogram
Fever chart or line graph
Project management / planning
Flowchart
Gantt chart (project management)
Maps
Nautical chart
Political theory
Nolan chart
Pournelle chart
Computation
The common methods for multiplying numbers using pencil and paper require a multiplication chart of memorized or consulted products of small numbers (typically any two numbers from 0 to 9), however one method, the peasant multiplication algorithm, does not.
Multiplying numbers to more than a couple of decimal places by hand is tedious and error prone. Common logarithms were invented to simplify such calculations. The slide rule allowed numbers to be quickly multiplied to about three places of accuracy. Beginning in the early twentieth century, mechanical calculators, such as the Marchant, automated multiplication of up to 10 digit numbers. Modern electronic computers and calculators have greatly reduced the need for multiplication by hand and the need for multiplication charts.
Additional information and source: Multiplication table