fraction

A package that helps you dealing with mathematical fractions.

  • Fraction which represents fractions in the form a/b;
  • MixedFraction which represents mixed fractions in the form a b/c

Working with fractions

You can create an instance of Fraction using one of its constructors.

  • Basic: it just requires the numerator and/or the denominator.

    final frac = Fraction(3, 5); // 3/5
    final frac = Fraction(3, 5); // 3/1
    
  • String: pass the fraction as a string but it has to be well-formed otherwise an exception is thrown.

    final frac1 = Fraction.fromString("2/4"); // 2/4
    final frac2 = Fraction.fromString("-2/4"); // -2/4
    final frac3 = Fraction.fromString("2/-4"); // Error
    final frac4 = Fraction.fromString("-2"); // -2/1
    
  • double: represents a double as a fraction. Note that irrational numbers cannot be converted into a fraction by definition; the constructor has the precision parameter which decides how precise the representation has to be.

    final frac1 = Fraction.fromDouble(1.5); // 3/2
    final frac2 = Fraction.fromString(-8.5); // -17/2
    final frac3 = Fraction.fromString(math.pi); // 208341/66317
    final frac4 = Fraction.fromString(math.pi, 1.0E-4); // 333/106
    

    The constant pi cannot be represented as a fraction because it's an irrational number. The constructor considers only precison decimal digits to create a fraction. With rational numbers instead you don't have problems.

Thanks to extension methods you can also create a Fraction object "on the fly" by calling the toFraction() method on a number or a string.

final f1 = 5.toFraction(); // 5/1
final f2 = 1.5.toFraction(); // 3/2
final f3 = "6/5".toFraction(); // 6/5

The class has a rich API that overloads a lot of operators, for arithmetics and comparisons. The method reduces reduces the fraction to the lowest terms.

final fraction = Fraction.fromString("12/20"); // 12/20
fraction.reduce(); // now it's simplified to  3/5

Two fractions are equal if their "cross product" is equal. For example 1/2 and 3/6 are said to be equivalent because 1*6 = 3*2 (and in fact 3/6 is the same as 1/2). You can get the numerator and the denominator either with getters...

    final fraction = Fraction(3, 10);
    final num = fraction.numerator; // 3
    final den = fraction.denominator; // 10

... or with the [] operator:

    final fraction = Fraction(3, 10);
    final num = fraction[0]; // 3
    final den = fraction[1]; // 10

Working with mixed fractions

A mixed fraction is made up of a whole part and a proper fraction (a fraction in which numerator <= denominator). It's easy to build a MixedFraction object:

final f1 = MixedFraction(3, 4, 7);
final f2 = MixedFraction.fromDouble(1.5);
final f3 = MixedFraction.fromString("1 1/2");

There is also the possibility to initialize a MixedFraction using extension methods:

final f1 = "1 1/2".toMixedFraction();

If you try to create an instance in which the numerator is greater than the denominator, a MixedFractionException is thrown.

Libraries

fraction