Rational Numbers

(Rational Numbers) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private instance variables of the class the numerator and the denominator. Provide a constructor that enables an object of this class to be initialized when it is declared. The constructor should store the fraction in reduced form. The fraction 2/4 is equivalent to 1/2 and would be stored in the object as 1 in the numerator and 2 in the denominator. Provide a no-argument constructor with default values in case no initializers are provided. Provide public methods that perform each of the following operations: a. Add two Rational numbers: The result of the addition should be stored in reduced form. b. Subtract two Rational numbers: The result of the subtraction should be stored in reduced form. c. Multiply two Rational numbers: The result of the multiplication should be stored in reduced form. d. Divide two Rational numbers: The result of the division should be stored in reduced form. e. Print Rational numbers in the form a/b, where a is the numerator and b is the denominator. f. Print Rational numbers in floating-point format. (Consider providing formatting capabilities that enable the user of the class to specify the number of digits of precision to the right of the decimal point.) – 提示： – 有理数是有分子、分母以形式a/b表示的数，其中a是分子，b是分母。例如，1/3，3/4，10/4。 – 有理数的分母不能为0，分子却可以为0。每个整数a等价于有理数a/1。有理数用于分数的精确计算中。例如1/3=0.0000…，它不能使用数据类型double或float的浮点格式精确表示出来，为了得到准确结果，必须使用有理数。 – Java提供了整数和浮点数的数据类型，但是没有提供有理数的类型。 – 由于有理数与整数、浮点数有许多共同特征，并且Number类是数字包装的根类，因此，把有理数类Rational定义为Number类的一个子类是比较合适的。由于有理数是可比较的，那么Rational类也应该实现Comparable接口。+下页图中描述了Rational类已将其与Number类和Comparable接口的关系。 – no-argument constructor with default values in case no initializers are provided. Provide public methods that perform each of the following operations: a. Add two Rational numbers: The result of the addition should be stored in reduced form. b. Subtract two Rational numbers: The result of the subtraction should be stored in reduced form. c. Multiply two Rational numbers: The result of the multiplication should be stored in reduced form. d. Divide two Rational numbers: The result of the division should be stored in reduced form. e. Print Rational numbers in the form a/b, where a is the numerator and b is the denominator. f. Print Rational numbers in floating-point format. (Consider providing formatting capabilities that enable the user of the class to specify the number of digits of precision to the right of the decimal point.) – 提示： – 有理数是有分子、分母以形式a/b表示的数，其中a是分子，b是分母。例如，1/3，3/4，10/4。 – 有理数的分母不能为0，分子却可以为0。每个整数a等价于有理数a/1。有理数用于分数的精确计算中。例如1/3=0.0000…，它不能使用数据类型double或float的浮点格式精确表示出来，为了得到准确结果，必须使用有理数。 – Java提供了整数和浮点数的数据类型，但是没有提供有理数的类型。 – 由于有理数与整数、浮点数有许多共同特征，并且Number类是数字包装的根类，因此，把有理数类Rational定义为Number类的一个子类是比较合适的。由于有理数是可比较的，那么Rational类也应该实现Comparable接口。+下页图中描述了Rational类已将其与Number类和Comparable接口的关系。 –