# 9.28 FractionΒΆ

The Fraction domain implements quotients. The elements must belong to a domain of category IntegralDomain: multiplication must be commutative and the product of two non-zero elements must not be zero. This allows you to make fractions of most things you would think of, but don’t expect to create a fraction of two matrices! The abbreviation for Fraction is FRAC.

Use / to create a fraction.

```
a := 11/12
```

1112 |

_{Type: Fraction Integer}

```
b := 23/24
```

2324 |

_{Type: Fraction Integer}

The standard arithmetic operations are available.

```
3 - a*b^2 + a + b/a
```

31327176032 |

_{Type: Fraction Integer}

Extract the numerator and denominator by using numernumerFraction and denomdenomFraction, respectively.

```
numer(a)
```

11 |

_{Type: PositiveInteger}

```
denom(b)
```

24 |

_{Type: PositiveInteger}

Operations like maxmaxFraction, minminFraction, negative?negative?Fraction, positive?positive?Fraction and zero?zero?Fraction are all available if they are provided for the numerators and denominators. See IntegerXmpPage for examples.

Don’t expect a useful answer from factorfactorFraction, gcdgcdFraction or lcmlcmFraction if you apply them to fractions.

```
r := (x^2 + 2*x + 1)/(x^2 - 2*x + 1)
```

x2+2x+1x2-2x+1 |

_{Type: Fraction Polynomial Integer}

Since all non-zero fractions are invertible, these operations have trivial definitions.

```
factor(r)
```

x2+2x+1x2-2x+1 |

_{Type: Factored Fraction Polynomial Integer}

Use mapmapFraction to apply factorfactorFraction to the numerator and denominator, which is probably what you mean.

```
map(factor,r)
```

(x+1)2(x-1)2 |

_{Type: Fraction Factored Polynomial Integer}

Other forms of fractions are available. Use continuedFraction to create a continued fraction.

```
continuedFraction(7/12)
```

_{Type: ContinuedFraction Integer}

Use partialFraction to create a partial fraction. See ContinuedFractionXmpPage and PartialFractionXmpPage for additional information and examples.

```
partialFraction(7,12)
```

1-322+13 |

_{Type: PartialFraction Integer}

Use conversion to create alternative views of fractions with objects moved in and out of the numerator and denominator.

```
g := 2/3 + 4/5*%i
```

23+45i |

_{Type: Complex Fraction Integer}

Conversion is discussed in detail in Section ugTypesConvertPage .

```
g :: FRAC COMPLEX INT
```

10+12i15 |

_{Type: Fraction Complex Integer}