js实现分数

实现分数表示和运算

在JavaScript中实现分数（Fraction）需要创建表示分数的数据结构，并实现相关运算方法（加减乘除、约分等）。以下是完整实现方案：

创建分数类

class Fraction {
  constructor(numerator, denominator = 1) {
    if (denominator === 0) throw new Error('Denominator cannot be zero');
    this.numerator = numerator;
    this.denominator = denominator;
    this.normalize();
  }
}

约分方法

normalize() {
  const gcd = this.findGCD(Math.abs(this.numerator), Math.abs(this.denominator));
  this.numerator /= gcd;
  this.denominator /= gcd;

  // 确保分母始终为正
  if (this.denominator < 0) {
    this.numerator *= -1;
    this.denominator *= -1;
  }
  return this;
}

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

加法运算

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

减法运算

subtract(other) {
  const newNumerator = this.numerator * other.denominator - other.numerator * this.denominator;
  const newDenominator = this.denominator * other.denominator;
  return new Fraction(newNumerator, newDenominator);
}

乘法运算

multiply(other) {
  return new Fraction(
    this.numerator * other.numerator,
    this.denominator * other.denominator
  );
}

除法运算

divide(other) {
  if (other.numerator === 0) throw new Error('Cannot divide by zero');
  return new Fraction(
    this.numerator * other.denominator,
    this.denominator * other.numerator
  );
}

转换为字符串

toString() {
  if (this.denominator === 1) return `${this.numerator}`;
  return `${this.numerator}/${this.denominator}`;
}

转换为小数

toDecimal() {
  return this.numerator / this.denominator;
}

使用示例

const a = new Fraction(1, 2);
const b = new Fraction(3, 4);

console.log(a.add(b).toString());      // 输出 "5/4"
console.log(a.subtract(b).toString()); // 输出 "-1/4"
console.log(a.multiply(b).toString()); // 输出 "3/8"
console.log(a.divide(b).toString());   // 输出 "2/3"
console.log(a.toDecimal());            // 输出 0.5

扩展功能

对于更完整的实现，可以添加以下方法：

• 比较方法（equals, compareTo）
• 绝对值方法（abs）
• 倒数方法（reciprocal）
• 幂运算方法（pow）

这种实现方式保持了分数的精确计算，避免了浮点数运算带来的精度问题，适合需要精确分数运算的场景（如数学计算、金融应用等）。