用java 创建一个Fraction类执行分数运算。要求如下： ①定义类的private成员变量：分子f1和分母£2： ②提供构造方法，创建分数； ③提供两个分数相加的运算方法； ④提供两个分数相减的运算方法； ⑤提供两个分数相乘的运算方法； ⑥提供两个分数相除的运算方法； ⑦以a/的形式打印Fraction数； ⑧以浮点数的形式打印Fraction数； ⑨主程序中创建分数，完成分数运算，输出结果

下面是Fraction类的实现：

public class Fraction {
    private int numerator; // 分子
    private int denominator; // 分母

    // 构造方法
    public Fraction(int numerator, int denominator) {
        if (denominator == 0) {
            throw new IllegalArgumentException("分母不能为0");
        }
        if (numerator == 0) {
            this.numerator = 0;
            this.denominator = 1;
        } else {
            int gcd = gcd(Math.abs(numerator), Math.abs(denominator)); // 求分子分母的最大公约数
            this.numerator = numerator / gcd;
            this.denominator = denominator / gcd;
            if (this.denominator < 0) { // 分母为负数时，将分子分母都取反
                this.numerator = -this.numerator;
                this.denominator = -this.denominator;
            }
        }
    }

    // 辗转相减法求最大公约数
    private int gcd(int a, int b) {
        if (a < b) {
            return gcd(b, a);
        }
        while (b != 0) {
            int r = a % b;
            a = b;
            b = r;
        }
        return a;
    }

    // 分数加法
    public Fraction add(Fraction other) {
        int newNumerator = this.numerator * other.denominator + other.numerator * this.denominator;
        int newDenominator = this.denominator * other.denominator;
        return new Fraction(newNumerator, newDenominator);
    }

    // 分数减法
    public Fraction subtract(Fraction other) {
        int newNumerator = this.numerator * other.denominator - other.numerator * this.denominator;
        int newDenominator = this.denominator * other.denominator;
        return new Fraction(newNumerator, newDenominator);
    }

    // 分数乘法
    public Fraction multiply(Fraction other) {
        int newNumerator = this.numerator * other.numerator;
        int newDenominator = this.denominator * other.denominator;
        return new Fraction(newNumerator, newDenominator);
    }

    // 分数除法
    public Fraction divide(Fraction other) {
        if (other.numerator == 0) {
            throw new IllegalArgumentException("除数不能为0");
        }
        int newNumerator = this.numerator * other.denominator;
        int newDenominator = this.denominator * other.numerator;
        return new Fraction(newNumerator, newDenominator);
    }

    // 以a/b的形式打印分数
    public String toString() {
        if (denominator == 1) {
            return Integer.toString(numerator);
        } else {
            return numerator + "/" + denominator;
        }
    }

    // 以浮点数的形式打印分数
    public double toDouble() {
        return (double) numerator / denominator;
    }
}

然后可以编写一个测试程序来测试Fraction类：

public class TestFraction {
    public static void main(String[] args) {
        Fraction f1 = new Fraction(1, 2);
        Fraction f2 = new Fraction(3, 4);

        // 分数加法
        Fraction sum = f1.add(f2);
        System.out.println(f1 + " + " + f2 + " = " + sum);

        // 分数减法
        Fraction diff = f1.subtract(f2);
        System.out.println(f1 + " - " + f2 + " = " + diff);

        // 分数乘法
        Fraction product = f1.multiply(f2);
        System.out.println(f1 + " * " + f2 + " = " + product);

        // 分数除法
        Fraction quotient = f1.divide(f2);
        System.out.println(f1 + " / " + f2 + " = " + quotient);

        // 以a/b的形式打印分数
        System.out.println(f1 + " = " + f1.toString());
        System.out.println(f2 + " = " + f2.toString());

        // 以浮点数的形式打印分数
        System.out.println(f1 + " = " + f1.toDouble());
        System.out.println(f2 + " = " + f2.toDouble());
    }
}

输出结果为：

1/2 + 3/4 = 5/4
1/2 - 3/4 = -1/4
1/2 * 3/4 = 3/8
1/2 / 3/4 = 2/3
1/2 = 1/2
3/4 = 3/4
1/2 = 0.5
3/4 = 0.75