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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
In other countries that use a comma as a decimal mark, either the period or a middle dot is used for multiplication. [ citation needed ] Historically, in the United Kingdom and Ireland, the middle dot was sometimes used for the decimal to prevent it from disappearing in the ruled line, and the period/full stop was used for multiplication.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division. [1]
The oldest known multiplication tables were used by the Babylonians about 4000 years ago. [2] However, they used a base of 60. [2] The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. [2] "Table of Pythagoras" on Napier's bones [3]
All the above multiplication algorithms can also be expanded to multiply polynomials. Alternatively the Kronecker substitution technique may be used to convert the problem of multiplying polynomials into a single binary multiplication. [30] Long multiplication methods can be generalised to allow the multiplication of algebraic formulae:
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