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The Rhind Mathematical Papyrus. An Egyptian fraction is a finite sum of distinct unit fractions, such as + +. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.
In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite ...
The ancient Egyptian military was responsible for defending Egypt against foreign invasion, and for maintaining Egypt's domination in the ancient Near East. The military protected mining expeditions to the Sinai during the Old Kingdom and fought civil wars during the First and Second Intermediate Periods.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
The first free kindergarten in the US was founded in 1870 by Conrad Poppenhusen, a German industrialist and philanthropist, who also established the Poppenhusen Institute. The first publicly financed kindergarten in the US was established in St. Louis in 1873 by Susan Blow.
The fraction 99 / 70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator. Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: [ 2 ]
Egyptian hieroglyphs, examples of logograms. In a written language, a logogram (from Ancient Greek logos 'word', and gramma 'that which is drawn or written'), also logograph or lexigraph, is a written character that represents a semantic component of a language, such as a word or morpheme.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
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