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# vtson's solution

## to Rational Numbers in the JavaScript Track

Published at Sep 03 2020 · 0 comments
Instructions
Test suite
Solution

#### Note:

This exercise has changed since this solution was written.

A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.

The absolute value `|r|` of the rational number `r = a/b` is equal to `|a|/|b|`.

The sum of two rational numbers `r1 = a1/b1` and `r2 = a2/b2` is `r1 + r2 = a1/b1 + a2/b2 = (a1 * b2 + a2 * b1) / (b1 * b2)`.

The difference of two rational numbers `r1 = a1/b1` and `r2 = a2/b2` is `r1 - r2 = a1/b1 - a2/b2 = (a1 * b2 - a2 * b1) / (b1 * b2)`.

The product (multiplication) of two rational numbers `r1 = a1/b1` and `r2 = a2/b2` is `r1 * r2 = (a1 * a2) / (b1 * b2)`.

Dividing a rational number `r1 = a1/b1` by another `r2 = a2/b2` is `r1 / r2 = (a1 * b2) / (a2 * b1)` if `a2 * b1` is not zero.

Exponentiation of a rational number `r = a/b` to a non-negative integer power `n` is `r^n = (a^n)/(b^n)`.

Exponentiation of a rational number `r = a/b` to a negative integer power `n` is `r^n = (b^m)/(a^m)`, where `m = |n|`.

Exponentiation of a rational number `r = a/b` to a real (floating-point) number `x` is the quotient `(a^x)/(b^x)`, which is a real number.

Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.

Implement the following operations:

• addition, subtraction, multiplication and division of two rational numbers,
• absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.

Your implementation of rational numbers should always be reduced to lowest terms. For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc. To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`. So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.

Assume that the programming language you are using does not have an implementation of rational numbers.

## Setup

Go through the setup instructions for Javascript to install the necessary dependencies:

https://exercism.io/tracks/javascript/installation

## Requirements

Please `cd` into exercise directory before running all below commands.

Install assignment dependencies:

``````\$ npm install
``````

## Making the test suite pass

Execute the tests with:

``````\$ npm test
``````

In the test suites all tests but the first have been skipped.

Once you get a test passing, you can enable the next one by changing `xtest` to `test`.

## Submitting Solutions

Once you have a solution ready, you can submit it using:

``````exercism submit rational-numbers.js
``````

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

## Exercise Source Credits

### rational-numbers.spec.js

``````import { Rational } from './rational-numbers';

test('Add two positive rational numbers', () => {
const expected = new Rational(7, 6);
});

xtest('Add a positive rational number and a negative rational number', () => {
const expected = new Rational(-1, 6);
});

xtest('Add two negative rational numbers', () => {
const expected = new Rational(-7, 6);
});

const expected = new Rational(0, 1);
});
});

describe('Subtraction', () => {
xtest('Subtract two positive rational numbers', () => {
const expected = new Rational(-1, 6);
expect(new Rational(1, 2).sub(new Rational(2, 3))).toEqual(expected);
});

xtest('Subtract a positive rational number and a negative rational number', () => {
const expected = new Rational(7, 6);
expect(new Rational(1, 2).sub(new Rational(-2, 3))).toEqual(expected);
});

xtest('Subtract two negative rational numbers', () => {
const expected = new Rational(1, 6);
expect(new Rational(-1, 2).sub(new Rational(-2, 3))).toEqual(expected);
});

xtest('Subtract a rational number from itself', () => {
const expected = new Rational(0, 1);
expect(new Rational(1, 2).sub(new Rational(1, 2))).toEqual(expected);
});
});

describe('Multiplication', () => {
xtest('Multiply two positive rational numbers', () => {
const expected = new Rational(1, 3);
expect(new Rational(1, 2).mul(new Rational(2, 3))).toEqual(expected);
});

xtest('Multiply a negative rational number by a positive rational number', () => {
const expected = new Rational(-1, 3);
expect(new Rational(-1, 2).mul(new Rational(2, 3))).toEqual(expected);
});

xtest('Multiply two negative rational numbers', () => {
const expected = new Rational(1, 3);
expect(new Rational(-1, 2).mul(new Rational(-2, 3))).toEqual(expected);
});

xtest('Multiply a rational number by its reciprocal', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 2).mul(new Rational(2, 1))).toEqual(expected);
});

xtest('Multiply a rational number by 1', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).mul(new Rational(1, 1))).toEqual(expected);
});

xtest('Multiply a rational number by 0', () => {
const expected = new Rational(0, 1);
expect(new Rational(1, 2).mul(new Rational(0, 1))).toEqual(expected);
});
});

describe('Division', () => {
xtest('Divide two positive rational numbers', () => {
const expected = new Rational(3, 4);
expect(new Rational(1, 2).div(new Rational(2, 3))).toEqual(expected);
});

xtest('Divide a positive rational number by a negative rational number', () => {
const expected = new Rational(-3, 4);
expect(new Rational(1, 2).div(new Rational(-2, 3))).toEqual(expected);
});

xtest('Divide two negative rational numbers', () => {
const expected = new Rational(3, 4);
expect(new Rational(-1, 2).div(new Rational(-2, 3))).toEqual(expected);
});

xtest('Divide a rational number by 1', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).div(new Rational(1, 1))).toEqual(expected);
});
});

describe('Absolute value', () => {
xtest('Absolute value of a positive rational number', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).abs()).toEqual(expected);
});

xtest('Absolute value of a negative rational number', () => {
const expected = new Rational(1, 2);
expect(new Rational(-1, 2).abs()).toEqual(expected);
});

xtest('Absolute value of zero', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 1).abs()).toEqual(expected);
});
});

describe('Exponentiation of a rational number', () => {
xtest('Raise a positive rational number to a positive integer power', () => {
const expected = new Rational(1, 8);
expect(new Rational(1, 2).exprational(3)).toEqual(expected);
});

xtest('Raise a negative rational number to a positive integer power', () => {
const expected = new Rational(-1, 8);
expect(new Rational(-1, 2).exprational(3)).toEqual(expected);
});

xtest('Raise zero to an integer power', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 1).exprational(5)).toEqual(expected);
});

xtest('Raise one to an integer power', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 1).exprational(4)).toEqual(expected);
});

xtest('Raise a positive rational number to the power of zero', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 2).exprational(0)).toEqual(expected);
});

xtest('Raise a negative rational number to the power of zero', () => {
const expected = new Rational(1, 1);
expect(new Rational(-1, 2).exprational(0)).toEqual(expected);
});
});

describe('Exponentiation of a real number to a rational number', () => {
xtest('Raise a real number to a positive rational number', () => {
const expected = 16.0;
expect(new Rational(4, 3).expreal(8)).toEqual(expected);
});

xtest('Raise a real number to a negative rational number', () => {
expect(new Rational(-1, 2).expreal(9)).toBeCloseTo(0.33, 2);
});

xtest('Raise a real number to a zero rational number', () => {
const expected = 1.0;
expect(new Rational(0, 1).expreal(2)).toEqual(expected);
});
});

describe('Reduction to lowest terms', () => {
xtest('Reduce a positive rational number to lowest terms', () => {
const expected = new Rational(1, 2);
expect(new Rational(2, 4).reduce()).toEqual(expected);
});

xtest('Reduce a negative rational number to lowest terms', () => {
const expected = new Rational(-2, 3);
expect(new Rational(-4, 6).reduce()).toEqual(expected);
});

xtest('Reduce a rational number with a negative denominator to lowest terms', () => {
const expected = new Rational(-1, 3);
expect(new Rational(3, -9).reduce()).toEqual(expected);
});

xtest('Reduce zero to lowest terms', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 6).reduce()).toEqual(expected);
});

xtest('Reduce an integer to lowest terms', () => {
const expected = new Rational(-2, 1);
expect(new Rational(-14, 7).reduce()).toEqual(expected);
});

xtest('Reduce one to lowest terms', () => {
const expected = new Rational(1, 1);
expect(new Rational(13, 13).reduce()).toEqual(expected);
});
});``````
``````//
// This is only a SKELETON file for the 'Rational Numbers' exercise. It's been provided as a
// convenience to get you started writing code faster.
//

export class Rational {
constructor(a, b) {
this.a = a;
this.b = b;
}

var valueA = this.a*newValue.b + newValue.a*this.b ;
var valueB = valueA ? this.b*newValue.b : 1;
return new Rational(valueA, valueB);
}

sub(newValue) {
var valueA = this.a*newValue.b - newValue.a*this.b ;
var valueB = valueA ? this.b*newValue.b : 1;
return new Rational(valueA, valueB);
}

mul(newValue) {
var valueA = this.a*newValue.a;
var valueB = this.b*newValue.b;
var gcd = this.gcd(valueA, valueB);
gcd = gcd < 0 ? -1*gcd : gcd;
return new Rational(valueA/gcd, valueB/gcd);

}

div(newValue) {
var valueA = this.a*newValue.b;
var valueB = this.b*newValue.a;
var gcd = this.gcd(valueA, valueB);
return new Rational(valueA/gcd, valueB/gcd);
}

abs() {
var valueA = Math.abs(this.a);
var valueB = Math.abs(this.b);
return new Rational(valueA, valueB);
}

exprational(exprational) {
var valueA = this.a**exprational;
var valueB = this.b**exprational;
return new Rational(valueA, valueB);
}

expreal(expreal) {
return (expreal**(this.a/this.b)).toPrecision(2)*1;
}

reduce() {
var gcd = this.gcd(this.a, this.b);
gcd = this.b < 0 ? -1*gcd : gcd;
var valueA = this.a;
var valueB = this.b;
return new Rational(valueA/gcd, valueB/gcd);
}

gcd(a, b) {
var tmp;
while(b != 0) {
tmp = a % b;
a = b;
b = tmp;
}
return a;
}

}``````