有理數是整數、分數的統稱。在Java中設計和實現有理數可以采用類的方式，一個有理數類應該含有以下屬性和方法：

public class RationalNumber {
private int numerator; // 分子
private int denominator; // 分母
public RationalNumber(int numerator, int denominator) {
this.numerator = numerator;
this.denominator = denominator;
}
public int getNumerator() {
return numerator;
}
public int getDenominator() {
return denominator;
}
public RationalNumber add(RationalNumber number) {
int newNumerator = numerator * number.getDenominator() + number.getNumerator() * denominator;
int newDenominator = denominator * number.getDenominator();
return new RationalNumber(newNumerator, newDenominator);
}
public RationalNumber subtract(RationalNumber number) {
int newNumerator = numerator * number.getDenominator() - number.getNumerator() * denominator;
int newDenominator = denominator * number.getDenominator();
return new RationalNumber(newNumerator, newDenominator);
}
public RationalNumber multiply(RationalNumber number) {
int newNumerator = numerator * number.getNumerator();
int newDenominator = denominator * number.getDenominator();
return new RationalNumber(newNumerator, newDenominator);
}
public RationalNumber divide(RationalNumber number) {
int newNumerator = numerator * number.getDenominator();
int newDenominator = denominator * number.getNumerator();
return new RationalNumber(newNumerator, newDenominator);
}
public String toString() {
return numerator + "/" + denominator;
}
}

在上面的代碼中，我們定義了有理數的分子和分母屬性，并且提供了加、減、乘、除四個操作的方法。在加減乘除時，需要注意分母的乘法操作和約分操作。同時，我們還定義了toString方法，用于將有理數轉換成字符串。

使用該有理數類，示例如下：

RationalNumber a = new RationalNumber(1, 2);
RationalNumber b = new RationalNumber(2, 3);
RationalNumber c = a.add(b);
RationalNumber d = a.subtract(b);
RationalNumber e = a.multiply(b);
RationalNumber f = a.divide(b);
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("a + b = " + c);
System.out.println("a - b = " + d);
System.out.println("a * b = " + e);
System.out.println("a / b = " + f);

運行結果如下：

a = 1/2
b = 2/3
a + b = 7/6
a - b = -1/6
a * b = 1/3
a / b = 3/4

以上示例展示了有理數的加減乘除操作，并且輸出了結果。