​​Lab 2: Big Fractions
​​Bard College – Computer Science – Data Structures
​​
​​In this lab, we will create a new user-defined type for doing math on Rational numbers, or in other terms, adding, subtracting, multiplying, and dividing fractions. 
​​
​​​​407409+409419+419421+421431=12261837304431095439321\frac{407}{409} + \frac{409}{419} + \frac{419}{421} + \frac{421}{431} = \frac{122618373044}{31095439321}​
​​
​​Rather than using int​ or  long​ as our underlying primitive datatype, we'll use BigInteger​ which is a little cumbersome, but allows exact arithmetic (i.e. no overflows).
​​
​​> 123456 * 123456
​​-1938485248
​​
​​> BigInteger.valueOf(123456).multiply(BigInteger.valueOf(123456))
​​1524138393
​​After all what good is a Fraction class that cannot add four simple fractions.
​​
​​Fraction f1 = new Fraction(407, 409);
​​Fraction f2 = new Fraction(409, 419);
​​Fraction f3 = new Fraction(419, 421);
​​Fraction f4 = new Fraction(421, 431);
​​System.out.println(f1.add(f2).add(f3).add(f4));
​​645226180/-343556083
​​
​​This is clearly a wrong answer. But BigInteger​ to the rescue.
​​
​​System.out.println(f1.add(f2).add(f3).add(f4));
​​122618373044/31095439321

​​A Rational Datatype: Fraction

​​First, let's introduce the Fraction​ interface (that you should not change):
​​
​​public class Fraction extends Number
​​    Fraction (BigInteger n, BigInteger d) throws IllegalArgumentException
​​    Fraction (BigInteger n) 
​​    Fraction (int n, int d)               throws IllegalArgumentException
​​    Fraction (int n)
​​    BigInteger getNumerator()
​​    BigInteger getDenominator()
​​    Fraction add(Fraction f)
​​    Fraction subtract(Fraction f)
​​    Fraction multiply(Fraction f)
​​    Fraction divide(Fraction f)
​​    boolean equals(Object o)
​​    String toString()
​​    static Fraction valueOf(int n, int d)
​​    double doubleValue()
​​    float floatValue()
​​    long longValue()
​​    int intValue()
​​    int compareTo(Fraction f) --- optional 
​​