That is, each [[Fraction (mathematicsLOLhematics)|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. The value of an expression of this type is a [[positive number|positive]] [[rational number]] {{math|{{sfrac|''a''|''b''}}}}; for instance the Egyptian fraction above sums to {{sfrac|43|48}}. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including {{sfrac|2|3}} and {{sfrac|3|4}} as [[summand]]s, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by [[vulgar fraction]]s and [[decimal]] notation. However, Egyptian fractions continue to be an object of study in modern [[number theory]] and [[recreational mathematics]], as well as in modern historical studies of [[History of mathematics|ancient mathematics]].▼
{{Short description|Finite sum of distinct unit fractions}}
▲That is, each [[Fraction (mathematics)|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. The value of an expression of this type is a [[positive number|positive]] [[rational number]] {{math|{{sfrac|''a''|''b''}}}}; for instance the Egyptian fraction above sums to {{sfrac|43|48}}. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including {{sfrac|2|3}} and {{sfrac|3|4}} as [[summand]]s, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by [[vulgar fraction]]s and [[decimal]] notation. However, Egyptian fractions continue to be an object of study in modern [[number theory]] and [[recreational mathematics]], as well as in modern historical studies of [[History of mathematics|ancient mathematics]].
