请用java实现7. Implement the class MixedNumber that you designed in the previous project. Use the operations in Fraction whenever possible. For example, to add two mixed numbers, convert them to fractions, add the fractions by using Fraction’s add operation, and then convert the resulting fraction to mixed form. Use analogous techniques for the other arithmetic operations. Handling the sign of a mixed number can be a messy problem if you are not careful. Mathematically, it makes sense for the sign of the integer part to match the sign of the fraction. But if you have a negative fraction, for example, the toString method for the mixed number could give you the string "−5 −1/2", instead of "−5 1/2", which is what you would normally expect. Here is a possible solution that will greatly simplify computations. Represent the sign of a mixed number as a character data field. Once this sign is set, make the integer and fractional parts positive. When a mixed number is created, if the given integer part is not zero, take the sign of the integer part as the sign of the mixed number and ignore the signs of the fraction’s numerator and denominator. However, if the given integer part is zero, take the sign of the given fraction as the sign of the mixed number.

以下是使用Java实现混合数的代码：

public class Fraction {
    private int numerator;
    private int denominator;

    // 构造函数
    public Fraction(int numerator, int denominator) {
        this.numerator = numerator;
        this.denominator = denominator;
        simplify();
    }

    // 约分
    private void simplify() {
        int gcd = gcd(numerator, denominator);
        numerator /= gcd;
        denominator /= gcd;
        if (denominator < 0) {
            numerator = -numerator;
            denominator = -denominator;
        }
    }

    // 求最大公约数
    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

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

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

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

    // 除法
    public Fraction divide(Fraction other) {
        int newNumerator = numerator * other.denominator;
        int newDenominator = denominator * other.numerator;
        return new Fraction(newNumerator, newDenominator);
    }

    // 转化为字符串形式
    public String toString() {
        if (denominator == 1) {
            return String.valueOf(numerator);
        } else {
            return numerator + "/" + denominator;
        }
    }
}

public class MixedNumber {
    private char sign;
    private int integerPart;
    private Fraction fractionPart;

    // 构造函数
    public MixedNumber(int integerPart, Fraction fractionPart) {
        this.sign = fractionPart.toString().charAt(0);
        if (integerPart != 0) {
            this.sign = (char) (integerPart > 0 ? '+' : '-');
            this.integerPart = Math.abs(integerPart);
        } else {
            this.integerPart = 0;
        }
        this.fractionPart = new Fraction(Math.abs(fractionPart.numerator), Math.abs(fractionPart.denominator));
    }

    // 加法
    public MixedNumber add(MixedNumber other) {
        Fraction f1 = toFraction();
        Fraction f2 = other.toFraction();
        Fraction newFraction = f1.add(f2);
        return new MixedNumber(0, newFraction);
    }

    // 减法
    public MixedNumber subtract(MixedNumber other) {
        Fraction f1 = toFraction();
        Fraction f2 = other.toFraction();
        Fraction newFraction = f1.subtract(f2);
        return new MixedNumber(0, newFraction);
    }

    // 乘法
    public MixedNumber multiply(MixedNumber other) {
        Fraction f1 = toFraction();
        Fraction f2 = other.toFraction();
        Fraction newFraction = f1.multiply(f2);
        return new MixedNumber(0, newFraction);
    }

    // 除法
    public MixedNumber divide(MixedNumber other) {
        Fraction f1 = toFraction();
        Fraction f2 = other.toFraction();
        Fraction newFraction = f1.divide(f2);
        return new MixedNumber(0, newFraction);
    }

    // 将混合数转化为分数
    private Fraction toFraction() {
        int newNumerator = integerPart * fractionPart.denominator + Math.abs(fractionPart.numerator);
        if (sign == '-') {
            newNumerator = -newNumerator;
        }
        return new Fraction(newNumerator, fractionPart.denominator);
    }

    // 转化为字符串形式
    public String toString() {
        String integerStr = (integerPart == 0 && fractionPart.numerator != 0) ? "" : String.valueOf(integerPart);
        String fractionStr = fractionPart.toString();
        if (integerPart == 0 && fractionPart.numerator == 0) {
            return "0";
        } else if (integerPart == 0) {
            return sign + fractionStr;
        } else if (fractionPart.numerator == 0) {
            return sign + integerStr;
        } else {
            return sign + integerStr + " " + fractionStr;
        }
    }
}