You need to work with fractions supplied by the user, such as 3 4/5 and 134/21. Your application needs to parse, multiply, and reduce fractions.

Use Commons Lang's Fraction class to parse and manipulate fractions. The following code demonstrates the parsing of a String containing a fraction:

import org.apache.commons.lang.math.Fraction;
String userInput = "23 31/37";
Fraction fraction = Fraction.getFraction( userInput );
double value = fraction.doubleValue( );

The String "23 31/37" is converted to a double value of 23.837837. A Fraction object is created by calling the Fraction.getFraction( ) method, and double value of the Fraction object is obtained with fraction.doubleValue( ).

The Fraction class provides a number of operations that can be used to simplify the following expression to an improper fraction. The following code evaluates the expression in Figure 8-1 using Fraction:

import org.apache.commons.lang.math.Fraction;
Fraction numer1 = Fraction.getFraction( 3, 4 );
Fraction numer2 = Fraction.getFraction( 51, 3509 );
Fraction numerator = numer1.multiplyBy( numer2 );
Fraction denominator = Fraction.getFraction( 41, 59 );
Fraction fraction = numerator.divideBy( denominator );
Fraction result = fraction.reduce( );
System.out.println( "as Fraction: " + result.reduce( ).toString( ) );
System.out.println( "as double: " + result.doubleValue( ) );

Figure 8-1. Expression to be evaluated with Fraction

The previous example creates an instance of Fraction by calling the static getFraction(int numerator, int denominator) method. Fraction objects are then multiplied and divided with the multiplyBy( ) and divideBy( ) methods of Fraction. And, the final call to reduce( ) reduces the Fraction to the smallest possible denominator. This example executes and prints the following output to the console:

Expression as Fraction: 9027/575476
Expression as double: 0.015686145034719084

An improper fraction is a fraction such that X/Y > 1 (i.e., "135/23" or "3/2"). Fraction provides the ability to convert improper fractions to proper fractions as demonstrated in the following example:

import org.apache.commons.lang.math.Fraction;
String userInput = "101/99";
String properString = Fraction.getFraction(userInput).toProperString( );
// properString is now "1 2/99"

Table 8-1 lists a sampling of methods available on the Fraction class.

For more information about downloading Commons Lang, see Recipe 1.1.