A package that helps you working with fractions and mixed fractions.
https://pub.dev/packages/fraction
Working with fractions
You can create an instance of Fraction
using one of its constructors:

Default: it just requires the numerator and/or the denominator.
Fraction(3, 5); // 3/5 Fraction(3, 1); // 3

fromString: requires a
String
representing a fraction.Fraction.fromString("2/4"); // 2/4 Fraction.fromString("2/4"); // 2/4 Fraction.fromString("2/4"); // Throws an exception Fraction.fromString("2"); // 2/1 Fraction.fromString("/3"); // Error

fromDouble: converts a
double
into a fraction. Note that irrational numbers cannot be converted into fractions by definition; the constructor has theprecision
parameter which decides how precise the representation has to be.Fraction.fromDouble(1.5); // 3/2 Fraction.fromDouble(8.5); // 17/2 Fraction.fromDouble(math.pi); // 208341/66317 Fraction.fromDouble(math.pi, precision: 1.0e4); // 333/106
The constant
pi
cannot be represented as a fraction because it's an irrational number. The constructor considers onlyprecison
decimal digits to create a fraction.
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.
5.toFraction(); // 5/1
1.5.toFraction(); // 3/2
"6/5".toFraction(); // 6/5
Note that a Fraction
object is immutable so methods that require changing the internal state of the object return a new instance. For example, the reduce()
method reduces the fraction to the lowest terms and returns a new instance:
final fraction = Fraction.fromString("12/20"); // 12/20
final reduced = fraction.reduce(); // 3/5
Fraction strings can be converted from and to unicode glyphs when possible.
Fraction.fromGlyph("¼"); // Fraction(1, 4)
Fraction(1, 2).toStringAsGlyph(); // "½"
You can easily sum, subtract, multiply and divide fractions thanks to arithmetic operators:
final f1 = Fraction(5, 7);
final f2 = Fraction(1, 5);
final sum = f1 + f2; // > 5/7 + 1/5
final sub = f1  f2; // > 5/7  1/5
final mul = f1 * f2; // > 5/7 * 1/5
final div = f1 / f2; // > 5/7 / 1/5
The Fraction
type has a wide API with the most common operations you'd expect to make on a fraction:
Fraction(10, 2).toDouble(); // 5.0
Fraction(10, 2).inverse(); // 2/10
Fraction(1, 15).isWhole; // false
Fraction(2, 3).negate(); // 2/3
Fraction(1, 15).isImproper; // false
Fraction(1, 15).isProper; // true
// Access numerator and denominator by index
final fraction = Fraction(7, 12);
print('${fraction[0]}'); // 7
print('${fraction[1]}'); // 12
Any other index value different from 0
and 1
throws a FractionException
exception. 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
).
Working with mixed fractions
A mixed fraction is made up of a whole part and a proper fraction (a fraction in which numerator <= denominator). Building a MixedFraction
object is very easy:
MixedFraction(
whole: 3,
numerator: 4,
denominator: 7
);
As it happens with fractions, you can use various named constructors as well:
MixedFraction.fromDouble(1.5);
MixedFraction.fromString("1 1/2");
There also is the possibility to initialize a MixedFraction
using extension methods:
final mixed = "1 1/2".toMixedFraction();
Note that MixedFraction
objects are immutable exactly like Fraction
objects so you're guaranteed that the internal state of the instance won't change. Make sure to check the official documentation at pub.dev for a complete overview of the API.
Egyptian fractions
An Egyptian fraction is a finite sum of distinct fractions where the numerator is always 1 and, the denominator is a positive number and all the denominators differ from each other. For example:
 5/8 = 1/2 + 1/8 (where "1/2 + 1/8" is the egyptian fraction)
In other words, egyptian fractions are a sum of fractions in the form 1/x that represent a proper or an improper fraction. Here's how they can be computed:
final egyptianFraction1 = Fraction(5, 8).toEgyptianFraction();
print("$egyptianFraction1"); // prints "1/2 + 1/8"
final egyptianFraction2 = MixedFraction(2, 4, 5).toEgyptianFraction();
print("$egyptianFraction2"); // prints "1 + 1 + 1/2 + 1/4 + 1/20"
The compute()
method returns an iterable.
Notes
Both Fraction
and MixedFraction
descend from the Rational
type which allows parsing both kind
of fractions with a single method call:
// This is a 'Fraction' object
Rational.tryParse('1/5'); // 1/5
// This is a 'MixedFraction' object
Rational.tryParse('2 4/7'); // 2 4/7
// This is 'null' because the string doesn't represent a fraction or a mixed fraction
Rational.tryParse(''); // null
Parsing integer values like Rational.tryParse('3')
always returns a Fraction
type but
it can easily be converted into a mixed fraction using the Fraction.toMixedFraction
method.
Libraries
 fraction
 A package that helps you working with fractions, mixed fractions and egyptian fractions.