js实现分数

分数表示方法

在JavaScript中，分数可以通过对象或类来表示。常见的方法是创建一个包含分子和属性的对象。

const fraction = {
  numerator: 3,
  denominator: 4
};

分数运算

实现基本的分数运算需要处理加减乘除以及约分。

function addFractions(a, b) {
  const numerator = a.numerator * b.denominator + b.numerator * a.denominator;
  const denominator = a.denominator * b.denominator;
  return simplify({ numerator, denominator });
}

function simplify(fraction) {
  const gcd = findGCD(fraction.numerator, fraction.denominator);
  return {
    numerator: fraction.numerator / gcd,
    denominator: fraction.denominator / gcd
  };
}

function findGCD(a, b) {
  return b === 0 ? a : findGCD(b, a % b);
}

类实现

使用ES6类可以更好地封装分数操作：

class Fraction {
  constructor(numerator, denominator) {
    this.numerator = numerator;
    this.denominator = denominator;
  }

  add(other) {
    const numerator = this.numerator * other.denominator + other.numerator * this.denominator;
    const denominator = this.denominator * other.denominator;
    return new Fraction(numerator, denominator).simplify();
  }

  simplify() {
    const gcd = this.findGCD(this.numerator, this.denominator);
    return new Fraction(this.numerator / gcd, this.denominator / gcd);
  }

  findGCD(a, b) {
    return b === 0 ? a : this.findGCD(b, a % b);
  }
}

使用示例

const frac1 = new Fraction(1, 2);
const frac2 = new Fraction(1, 4);
const result = frac1.add(frac2); // 返回 3/4

注意事项

处理分数时需要考虑分母为零的情况，应在构造函数中添加验证：

constructor(numerator, denominator) {
  if (denominator === 0) throw new Error('Denominator cannot be zero');
  this.numerator = numerator;
  this.denominator = denominator;
}

负分数通常将负号放在分子上，可以在简化时处理：

simplify() {
  let numerator = this.numerator;
  let denominator = this.denominator;

  if (denominator < 0) {
    numerator *= -1;
    denominator *= -1;
  }

  const gcd = this.findGCD(Math.abs(numerator), Math.abs(denominator));
  return new Fraction(numerator / gcd, denominator / gcd);
}