[1]Fraction simpler(Fraction f);//分数化简
[2]Fraction[] RCD(Fraction f1, Fraction f2);//通分
[3]int GCD(int s, int b);//最大公约数
[4]int LCM(int a, int b);//最小公倍数

[1]在控制台输入[分数][回车] //化简
[2]在控制台输入[分数][空格][运算符][空格][分数][回车] //计算

Fraction.java
package net.zj.fraction;

import java.io.IOException;

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

public Fraction(int numerator, int denominator) {
this.numerator = numerator;
this.denominator = denominator;
}

public Fraction(int numerator) {
this(numerator, 1);
}

public static Fraction add(Fraction f1, Fraction f2) {
Fraction[] fs = RCD(f1, f2);
Fraction add = new Fraction(fs[0].numerator + fs[1].numerator,
fs[0].denominator);
}

public static Fraction minus(Fraction f1, Fraction f2) {
Fraction[] fs = RCD(f1, f2);
Fraction minus = new Fraction(fs[0].numerator - fs[1].numerator,
fs[0].denominator);
return simpler(minus);
}

public static Fraction multi(Fraction f1, Fraction f2) {
Fraction multi = new Fraction(f1.numerator * f2.numerator,
f1.denominator * f2.denominator);
return simpler(multi);
}

public static Fraction div(Fraction f1, Fraction f2) {
return multi(f1, new Fraction(f2.denominator, f2.numerator));
}

public static void input(String s) {
String[] ss = s.split(" ");
if (ss.length == 1) {
Fraction f = StringToFraction(ss[0]);
if (f == null)
output("Usage: Should input a numeric");
else
output(f);
} else if (ss.length == 3) {
Fraction f1 = StringToFraction(ss[0]);
Fraction f2 = StringToFraction(ss[2]);
if (f1 == null) {
output("Usage: The first input should be numeric/numeric");
return;
}
if (f2 == null) {
output("Usage: The third input should be numeric/numeric");
return;
}
switch (ss[1].charAt(0)) {
case '+':
break;
case '-':
output(minus(f1, f2));
break;
case '*':
output(multi(f1, f2));
break;
case '/':
output(div(f1, f2));
break;
default:
output("Usage: The second input should be one of +-*/");
break;
}
} else
output("Usage: Should input one fraction or two fractions and a operator with the style 'f1 + f2'");
}

public static void output(Fraction f) {
if (f.denominator == 1) {
System.out.println(f.numerator);
return;
}
StringBuilder sb = new StringBuilder();
sb.append(f.numerator);
sb.append('/');
sb.append(f.denominator);
System.out.println(sb.toString());
}

public static void output(String s) {
System.out.println(s);
}

private static Fraction StringToFraction(String s) {
String[] ss = s.split("/");
try {
if (ss.length == 2)
return simpler(new Fraction(Integer.valueOf(ss[0]), Integer
.valueOf(ss[1])));
else if (ss.length == 1)
return new Fraction(Integer.valueOf(ss[0]));
else
return null;
} catch (NumberFormatException e) {
output("Usage: Should input one fraction or two fractions and a operator with the style 'f1 + f2'");
}
return null;
}

/**
* both the numerator and denominator are divided by GCD
*/

private static Fraction simpler(Fraction f) {
int gcd = GCD(f.numerator, f.denominator);
if (gcd > 1)
return new Fraction(f.numerator / gcd, f.denominator / gcd);
else
return f;
}

/**
* reduction to common denominator
*/

private static Fraction[] RCD(Fraction f1, Fraction f2) {
int lcm = LCM(f1.denominator, f2.denominator);
int m = lcm / f1.denominator;
if (m > 1)
f1 = new Fraction(f1.numerator * m, f1.denominator * m);
m = lcm / f2.denominator;
if (m > 1)
f2 = new Fraction(f2.numerator * m, f2.denominator * m);
return new Fraction[] { f1, f2 };
}

/**
* greatest common divisor
*/

private static int GCD(int s, int b) {
// s-small,b-big
if (s > b) {
int temp = s;
s = b;
b = temp;
}
while (b != 0) {
int temp = s % b;
s = b;
b = temp;
}
return s;
}

/**
* a lowest common multiple
*/

private static int LCM(int a, int b) {
return a * b / GCD(a, b);
}

public static void main(String[] args) throws IOException {
int c;
StringBuilder sb = new StringBuilder();
while ((c = System.in.read()) != '\n')
sb.append((char) c);
input(sb.toString());
}
}