##Learning Competencies
- Use Pseudocode effectively to model problem-solving
- Model a simple real-world system in Ruby code
- Identify and implement classes based on real world requirements
##Summary
We're going to model a system whose rules you've known for years and years: the arithmetic of the rational numbers.
As a quick refresher, a rational number is any number which can be expressed as the ratio of two integers. Read the Wikipedia page on the Rationals.
We're going to learn how to implement a more abstract system in code, but gain something in the process. By having our own "rational number class" we can perform exact arithmetic without the rounding errors that come from floating point arithmetic.
Think back to your calculator-using days when you'd type something like
1/3 + 1/3 + 1/3
and get back
1.00000000000001
We'll write code that will work like this:
num1 = RationalNumber.new(2,3)
num2 = RationalNumber.new(1,3)
# true
num1 + num2 == RationalNumber.new(1,1)##Releases
###Release 0 : Write down the rules of rational arithmetic
Read the Wikipedia page on the arithmetic of the Rationals. We're going to implement the following operations:
- Addition
- Subtraction
- Multiplication
- Division
- Equality
- Exponentiation
- Inversion / negation
- Reciprocation
Make sure you understand the rules. Use examples on pen and paper and make sure you can, say, add two rational numbers by hand.
###Release 1 : Fill in the RationalNumber class
You've been provided with a skeleton RationalNumber class with methods to fill in. Assume the input is always another RationalNumber instance. Ruby has a built-in Rational class; don't use it!
The point of this challenge is to see how something like Ruby's Rational might be implemented on the inside, and also to see how object-oriented design can implement concrete and abstract systems alike.
##Resources