$4\mathrm{.}12$ LAB $3$: Classes $($Rational$)$

Rational Numbers

It may come as a bit of a surprise when the C$++$ floating$-$point types $($float$,$ double$),$ fail to capture a particular value accurately. Certainly double, which is usually stored as a $64-$bit value, is far better than the old float, which is only $32$ bits, but problems do arise. For example:

float n $=2\mathrm{.}0$;

float d $=3\mathrm{.}0$;

cout $<<$ precision$(17)$;

cout $<<$ n $/$ d $<<$ endl;

produces $0\mathrm{.}6666668653488159,$ which is accurate to only $8$ decimal places $-$ a bit dirty for a discipline that prides itself on precision!

A solution that is often used when precision is of greatest importance and all of the numbers involved are going to be "rational" $($that is$,$ expressible as a 'ratio' of two integers $-$ i$.$e$.$ a fraction$)$ is to use a custom data type $-$ i$.$e$.$ a class $-$ that implements fractions, or "rational numbers". This is what you will do in this lab assignment.

Class Specification

Write a C$++$ program that performs the rational number operations addition, subtraction, multiplication and division on two fractions. The program should be written in a single file. You will need to design a "rational number" class named Rational whose value will be a fraction $($e$.$g$.,1/128,$ or $22/7),$ with appropriate constructors and member functions. A fraction will be specified as a numerator and a denominator $-$ e$.$g$.$ the pair $(8,109)$ represents the fraction $8/109.$ The member variables should be private and accessed using the accessor and mutator functions.

Constructors

Create $3$ constructors:

a constructor with two parameters $($numerator and denominator$)$

a constructor with one parameter $($denominator set to $1)$

a constructor with no parameters $(0/1)$

Accessor Functions

add

subtract

multiply

divide

display

Mutator Function

simplify

The following are a list of the rules of arithmetic for fractions:

$($a$/$b$)+($c$/$d$)=($ad $+$ bc$)/($b$*$d$)$

$($a$/$b$)-($c$/$d$)=($ad $-$ bc$)/($b$*$d$)$

$($a$/$b$)*($c$/$d$)=($ac$)/($bd$)$

$($a$/$b$)/($c$/$d$)=($ad$)/($cb$)$

Note that for this lab, when you perform an operation, you do not need to simplify the resulting fraction, i$.$e$.,4/5*5/10=20/50.$ You should not simplify this to $2/5$ at this point.

The display function should output the Rational object in the format:

n $/$ d

#include

using namespace std;

$//$ Rational Class declaration

class Rational $\{$

private:

int numerator;

int denominator;

public:

Rational$()$;

explicit Rational$($int$)$;

Rational$($int$,$ int$)$;

Rational add$($const Rational &$)$ const;

Rational subtract$($const Rational &$)$ const;

Rational multiply$($const Rational &$)$ const;

Rational divide$($const Rational &$)$ const;

void simplify$()$;

void display$()$ const;

private:

int gcd$($int$,$ int$)$ const;

$\}$;

$//$ Implement Rational class member functions here

$//$ Do not change any of the code below this line!!

Rational getRational$()$;

void displayResult$($const string &$,$ const Rational &$,$ const Rational&$,$ const Rational&$)$;

int main$()\{$

Rational A$,$ B$,$ result;

char choice;

cout $<<$ "Enter Rational A:$"<<$ endl;

A $=$ getRational$()$;

cout $<<$ endl;

cout $<<$ "Enter Rational B:$"<<$ endl;

B $=$ getRational$()$;

cout $<<$ endl;

cout $<<$ "Enter Operation:" $<<$ endl

$<<"$a $-$ Addition $($A $+$ B$)"<<$ endl

$<<"$s $-$ Subtraction $($A $-$ B$)"<<$ endl

$<<"$m $-$ Multiplication $($A $*$ B$)"<<$ endl

$<<"$d $-$ Division $($A $/$ B$)"<<$ endl

$<<"$y $-$ Simplify A$"<<$ endl;

cin $>>$ choice;

cout $<<$ endl;

if $($choice $==\text{'}$a$\text{'})\{$

result $=$ A$.$add$($B$)$;

displayResult$("+",$ A$,$ B$,$ result$)$;

$\}$ else if $($choice $==\text{'}$s$\text{'})\{$

result $=$ A$.$subtract$($B$)$;

displayResult$("-",$ A$,$ B$,$ result$)$;

$\}$ else if $($choice $==\text{'}$m$\text{'})\{$

result $=$ A$.$multiply$($B$)$;

displayResult$("*",$ A$,$ B$,$ result$)$;

$\}$ else if $($choice $==\text{'}$d$\text{'})\{$

result $=$ A$.$divide$($B$)$;

displayResult$("/",$ A$,$ B$,$ result$)$;

$\}$ else if $($choice $==\text{'}$y$\text{'})\{$

A$.$simplify$()$;

A$.$display$()$;

$\}$ else $\{$

cout $<<$ "Unknown Operation";

$\}$

cout $<<$ endl;

return $0$;

$\}$

Rational getRational$()\{$

int choice;

int numer, denom;

cout $<<$ "Which Rational constructor? $($Enter $2,1,$ or $0)"<<$ endl

$<<"2-2$ parameters $($numerator & denominator$)"<<$ endl

$<<"1-1$ parameter $($numerator$)"<<$ endl

$<<"0-0$ parameters $($default$)"<<$ endl;

cin $>>$ choice;

cout $<<$ endl;

if $($choice $==2)\{$

cout $<<$ "numerator? $"$;

cin $>>$ numer;

cout $<<$ endl;

cout $<<$ "denominator? $"$;

cin $>>$ denom;

cout $<<$ endl;

return Rational$($numer$,$ denom$)$;

$\}$ else if $($choice $==1)\{$

cout $<<$ "numerator? $"$;

cin $>>$ numer;

cout $<<$ endl;

return Rational$($numer$)$;

$\}$ else $\{$

return Rational$()$;

$\}$

$\}$

void displayResult$($const string &op$,$ const Rational &lhs$,$ const Rational&rhs$,$ const Rational &result$)\{$

cout $<<"("$;

lhs$.$display$()$;

cout $<<")"<<$ op $<<"("$;

rhs$.$display