A

**fraction**(from Latin:**fractus**, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
A

**common**or**vulgar**fraction, such as , ,and consists of an integer**numerator**and a non-zero integer**denominator**—the numerator representing a number of equal parts and the denominator indicating how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts equal a whole. The picture to the right illustrates or 3/4 of a cake.
Fractional numbers can also be written without using explicit
numerators or denominators, by using decimals, percent signs, or negative
exponents (as in 0.01, 1%, and 10

^{−2}respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implied denominator of one: 7 equals 7/1.
Other uses for fractions are to represent ratios and
to represent division.

^{[1]}Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).
In mathematics the set of all numbers which can be expressed in
the form a/b, where a and b are integers and
b is not zero, is called the set of rational numbers and is represented by the symbol

**Q**, which stands for quotient. The test for a number being a rational number is that it can be written in that form (i.e., as a common fraction). However, the word*fraction*is also used to describe mathematical expressions that are not rational numbers, for example algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational).
A

**fraction**(from Latin:**fractus**, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
A

**common**or**vulgar**fraction, such as , ,and consists of an integer**numerator**and a non-zero integer**denominator**—the numerator representing a number of equal parts and the denominator indicating how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts equal a whole. The picture to the right illustrates or 3/4 of a cake.
Fractional numbers can also be written without using explicit
numerators or denominators, by using decimals, percent signs, or negative
exponents (as in 0.01, 1%, and 10

^{−2}respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implied denominator of one: 7 equals 7/1.
Other uses for fractions are to represent ratios and
to represent division.

^{[1]}Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).
In mathematics the set of all numbers which can be expressed in
the form a/b, where a and b are integers and
b is not zero, is called the set of rational numbers and is represented by the symbol

**Q**, which stands for quotient. The test for a number being a rational number is that it can be written in that form (i.e., as a common fraction). However, the word*fraction*is also used to describe mathematical expressions that are not rational numbers, for example algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational).
A

**fraction**(from Latin:**fractus**, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
A

**common**or**vulgar**fraction, such as , ,and consists of an integer**numerator**and a non-zero integer**denominator**—the numerator representing a number of equal parts and the denominator indicating how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts equal a whole. The picture to the right illustrates or 3/4 of a cake.
Fractional numbers can also be written without using explicit
numerators or denominators, by using decimals, percent signs, or negative
exponents (as in 0.01, 1%, and 10

^{−2}respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implied denominator of one: 7 equals 7/1.
Other uses for fractions are to represent ratios and
to represent division.

^{[1]}Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).
In mathematics the set of all numbers which can be expressed in
the form a/b, where a and b are integers and
b is not zero, is called the set of rational numbers and is represented by the symbol

**Q**, which stands for quotient. The test for a number being a rational number is that it can be written in that form (i.e., as a common fraction). However, the word*fraction*is also used to describe mathematical expressions that are not rational numbers, for example algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational).
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