fraction

A package that helps you work with fractions and mixed fractions.

🌎 https://pub.dev/packages/fraction

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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 a double value. Note that irrational numbers cannot be converted into fractions by definition. The constructor has the precision 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: 1.0e-4); // 333/106
  

  For example, the constant pi cannot be represented as a fraction because it's an irrational number. The constructor considers only precison 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("¼"); // Fraction(1, 4)
Fraction(1, 2).toStringAsGlyph(); // "½"

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 a List<Fraction> object.

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.