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A package that helps you work with fractions and mixed fractions.
A package that helps you work with fractions and mixed fractions.
π https://pub.dev/packages/fraction
Working with fractions #
You can create new Fraction
objects using one of its constructors:

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

fromString: requires a
String
that represents 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: creates a
Fraction
from adouble
value. 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
For example, the constant
pi
cannot be represented as a fraction because it's an irrational number. The constructor considers onlyprecison
decimal digits to create the fraction.
Thanks to extension methods, you can 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
The Fraction
type is immutable, so methods that require changing the object's internal state return a new instance. For example, the reduce()
method reduces the fraction to the lowest terms and returns a new object:
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. For example:
Fraction.fromGlyph("ΒΌ"); // Fraction(1, 4)
Fraction(1, 2).toStringAsGlyph(); // "Β½"
You can easily sum, subtract, multiply and divide fractions using arithmetic operators:
final f1 = Fraction(5, 7); // 5/7
final f2 = Fraction(1, 5); // 1/5
final sum = f1 + f2; // 32/35
final sub = f1  f2; // 18/35
final mul = f1 * f2; // 1/7
final div = f1 / f2; // 25/7
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
In the last example, any other 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 the Fraction
type, you can use various named constructors:
MixedFraction.fromDouble(1.5);
MixedFraction.fromString("1 1/2");
You can create new MixedFraction
objects using extension methods:
final mixed = "1 1/2".toMixedFraction();
The MixedFraction
type is immutable, as it happens with Fraction
. As such, you're guaranteed that the internal object state will never 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, the denominator is a positive number, and all the denominators differ. 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 toEgyptianFraction()
method returns an Iterable
.
Notes #
Note that Fraction
and MixedFraction
are subtypes of Rational
, which can be used for parsing both of kinds of fractions with a single method call. For example:
// Returns a 'Fraction' object
Rational.tryParse('1/5'); // 1/5
// Returns a 'MixedFraction' object
Rational.tryParse('2 4/7'); // 2 4/7
// This is 'null' because the string doesn't represent a valid fraction or mixed fraction
Rational.tryParse(''); // null
Parsing integer values such as Rational.tryParse('3')
always returns a Fraction
type.