Practical Work

Using Jupyter Notebook or other Python development platform, develop an object$-$oriented application that processes fractions. While you are responsible for the application's final design, your application is expected to contain a class called fraction, which represents the general format of a mixed fraction, i$.$e$.\backslash ($ i $\backslash$frac$\{$n$\}\{$d$\}\backslash ),$ where $\backslash ($ i $\backslash )$ is an optional integer part, $\backslash ($ n $\backslash )$ is the numerator and $\backslash ($ d $\backslash )$ the denominator. You can assume that all numbers $\backslash ($ i $\backslash ),\backslash ($ n $\backslash )$ and $\backslash ($ d $\backslash )$ are integers, and you do not need to check for this. Note that $\backslash ($ d $\backslash )$ must be positive. If $\backslash ($ d $\backslash )$ is zero, the number is undefined. If $\backslash ($ i $\backslash )$ is zero, then $\backslash ($ n $\backslash )$ may be negative, zero, or positive. However, if $\backslash ($ i $\backslash )$ is non$-$zero $($positive or negative$),\backslash ($ n $\backslash )$ must be non$-$negative, and. If $\backslash ($ n $\backslash )$ is zero, the fractional part does not exist and it reduces to the simple integer $\backslash ($ i $\backslash ).$ The general output format will be i$.$n$/$d$.$ Within the class, you must write public member function$($s$)$ to realize one of the following five tasks. The task to do should be determined by a hash function, $\backslash (\backslash$boldsymbol$\{$h$\}\backslash )($groupNo$,$ sid$1,$ sid$2,$ sid$3),$ taking inputs from the group number $($a number of two digits$),$ and the numeric digits of the sid of the students in the group. The hash function $\backslash (\backslash$boldsymbol$\{$h$\}()\backslash )$ will be provided after the groups are formed.

Tasks

$1)$ The member function $+$ performs the addition with another fraction and returns the result as a fraction. This is realized by implementing adc $()$ inside the class. The result need NOT be in its simplest form $($e$.$g$.,\backslash (4/10\backslash )$ need not be expressed as $\backslash (2/5\backslash )).$

$2)$ The member function $-$ performs a subtraction with another fraction and returns the result as a fraction. This is realized by implementing sub $()$ inside the class. The result need NOT be in its simplest form $($e$.$g$.,\backslash (4/10\backslash )$ need not be expressed as $\backslash (2/5\backslash )).$

$3)$ The member function $*$ performs a multiplication with another fraction and returns the result as a fraction. This is realized by implementing $\backslash (\backslash$mathrm$\{$mu$\}]\backslash )$

$()$ inside the class. The result has to be in its simplest form, i$.$e$.,$ any common factors between the numerator and the denominator should be canceled out. For example, if this fraction has $\backslash ($ n$=12\backslash )$ and $\backslash ($ d$=48\backslash ),$ the fraction to be multiplied has $\backslash ($ n$=6\backslash )$ and $\backslash ($ d$=16\backslash ),$ the method should return $\backslash (12/48\backslash$times $6/16=72/768=3/32\backslash ),$ i$.$e$.$ a fraction of $\backslash ($ n$=3\backslash )$ and $\backslash ($ d$=32\backslash )$ in its simplest form as $24$ is the highest common factor $($HCF$)$ of $72$ and $768.$

$4)$ The member function $/$ performs a division with another fraction and returns the result as a fraction. This is realized by implementing truediv $()$ inside the class. The result has to be in its simplest form, i$.$e$.,$ any common factors between the numerator and the denominator should be canceled out. For example, if this fraction has $\backslash ($ n$=12\backslash )$ and $\backslash ($ d$=48\backslash ),$ the fraction to be divided has $\backslash ($ n$=6\backslash )$ and $\backslash ($ d$=16\backslash ),$ the method should return $\backslash (12/48\backslash$div $6/16=192/288=2/3\backslash ),$ i$.$e$.$ a fraction of $\backslash ($ n$=2\backslash )$ and $\backslash ($ d$=3\backslash )$ in its simplest form as $96$ is the highest common factor $($HCF$)$ of $192$ and $288.$ It can be assumed that the divisor is not zero.

$5)$ The member function @ performs a comparison with another fraction. It returns the integer value $0$ if the other fraction is the same in value. It returns the integer value $-1$ if the other fraction is bigger $($i$.$e$.$ this fraction is smaller$).$ It returns the integer value $1$ if the other fraction is smaller $($i$.$e$.$ this fraction is bigger$).$ This is realized by implementing matmul $()$ inside the class.

Some sample program lines and execution results $($for reference only$)$:

$```$

f$1=$ fraction$(2,3,4)\backslash$ f$5=$ fraction$(1,11,12)$

f$2=$ fraction$(1,3,6)$ f$6=$ fraction$(2,19,24)$

f$3=$ fraction$(-2,3,4)\{7=$ fraction$(-1,11,12)$

f$4=$ fraction$(-1,3,6)\{$

print$("\{\}+\{\}=\{\}".$format$($f$1,$f$2,$f$1+$ f$2))$ print$("\{\}$ @ $\{\}=\{\}".$format$($f$5,$f$6,$f$5$@f$6))$

print$("\{\}+\{\}=\{\}".$format$($f$1,$f$4,$f$1+$ f$4))$ print$("\{\}$ @ $\{\}=\{\}".$format$($f$5,$f$8,$f$5$@f$8))$

print$("\{\}+\{\}=\{\}".$format$($f$3,$f$2,$f$3+$ f$2))$ print$("\{\}$ @ $\{\}=\{\}".$format$($f$7,$f$6,$f$7$@f$6))$

print$("\{\}+\{\}=\{\}".$format$($f$3,$f$4,$f$3+$ f$4))$ print$("\{\}$ @ $\{\}=\{\}".$format$($f$7,$f$8,$f$7$@f$8))$

$...\backslash ..$

f$9=$ fraction$(1,12,48)$

p $=3$

print$("\{\}**\{\}=\{\}".$format$($f$9,$p$,$f$9**$ p$))$

print$("\{\}/\{\}=\{\}".$format$($f$3,$f$2,$f$3/$ f$2))$

print$("\{\}/\{\}=\{\}".$format$($f$3,$f$4,$f$3/$ f$4))$

$``````$

$2\mathrm{.}3/4+1\mathrm{.}3/6=4\mathrm{.}1/4$

$2\mathrm{.}3/4+-1\mathrm{.}3/6=1\mathrm{.}1/4$

$-2\mathrm{.}3/4+1\mathrm{.}3/6=-1\mathrm{.}1/4$

$-2\mathrm{.}3/4+-1\mathrm{.}3/6=-4\mathrm{.}1/4$

$2\mathrm{.}3/4-1\mathrm{.}3/6=1\mathrm{.}1/4$

$2\mathrm{.}3/4--1\mathrm{.}3/6=4\mathrm{.}1/4$

$-2\mathrm{.}3/4-1\mathrm{.}3/6=-4\mathrm{.}1/4$

$-2\mathrm{.}3/4--1\mathrm{.}3/6=-1\mathrm{.}1/4$

$2\mathrm{.}3/4*1\mathrm{.}3/6=4\mathrm{.}1/8$

$2\mathrm{.}3/4*-1\mathrm{.}3/6=-4\mathrm{.}1/8$

$-2\mathrm{.}3/4*1\mathrm{.}3/6=-4\mathrm{.}1/8$

$-2\mathrm{.}3/4*-1\mathrm{.}3/6=4\mathrm{.}1/8$

$2\mathrm{.}3/4/1\mathrm{.}3/6=1\mathrm{.}5/6$

$2\mathrm{.}3/4/-1\mathrm{.}3/6=-1\mathrm{.}5/6$

$-2\mathrm{.}3/4/1\mathrm{.}3/6=-1\mathrm{.}5/6$

$-2\mathrm{.}3/4/-1\mathrm{.}3/6=1\mathrm{.}5/6$

$1\mathrm{.}11/12$ @ $2\mathrm{.}19/24=-1$

$1\mathrm{.}11/12$ @ $-2\mathrm{.}19/24=1$

$-1\mathrm{.}11/12$ @ $2\mathrm{.}19/24=-1$

$-1\mathrm{.}11/12$ @ $-2\mathrm{.}19/24=1$

$3\mathrm{.}4/12$ @ $3\mathrm{.}2/8=1$

$3\mathrm{.}4/12$ @ $-3\mathrm{.}2/8=1$

$-3\mathrm{.}4/12$

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