Lab 2: Big Fractions

Bard College – Computer Science – Data Structures

In this lab, we will create a new user-defined type for doing arithmetic on Rational numbers, or put in other terms: adding, subtracting, multiplying, and dividing fractions.

\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 data type, we'll use BigInteger which is a little cumbersome, but allows exact arithmetic (i.e. no overflows).

jshell> 123456 * 123456

-1938485248

jshell> 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

// creates a new fraction with the numerator n and denominator d

// throw an exception if the denominator is zero

Fraction (BigInteger n)

// creates a new fraction with the numerator n and denominator 1

Fraction (int n, int d) throws IllegalArgumentException

// creates a new fraction with the numerator n and denominator d

// throw an exception if the denominator is zero

Fraction (int n)

// creates a new fraction with the numerator n and denominator 1

BigInteger getNumerator()

// returns the numerator

​​A Rational Datatype: Fraction

A Rational Datatype: Fraction