如何简化分数？

Question

如何简化C#中的分数？例如,给定1 11/6,我需要简化为2 5/6.

Answer 1

如果你想要的只是将你的分数变成一个混合数,其小数部分是一个合适的分数,就像前面给出的答案一样,你只需要加上数字numerator / denominator的整个部分并将分子设置为numerator % denominator.使用循环完全没必要.

然而,术语"简化"通常是指将分数减少到其最低项.你的例子并没有说清楚你是否也想要这样,因为这个例子无论如何都是最低的.

这是一个C#类,它对一个混合数进行归一化,这样每个数字只有一个表示:小数部分始终是正确的,总是在最低的条件下,分母总是正的,整个部分的符号总是与分子的标志.

using System;

public class MixedNumber {
    public MixedNumber(int wholePart, int num, int denom)
    {  
        WholePart = wholePart;
        Numerator = num;
        Denominator = denom;
        Normalize();
    }

    public int WholePart { get; private set; }
    public int Numerator { get; private set; }
    public int Denominator { get; private set; }

    private int GCD(int a, int b)
    {  
        while(b != 0)
        {  
            int t = b;
            b = a % b;
            a = t;
        }
        return a;
    }

    private void Reduce(int x) {
        Numerator /= x;
        Denominator /= x;
    }

    private void Normalize() {
        // Add the whole part to the fraction so that we don't have to check its sign later
        Numerator += WholePart * Denominator;

        // Reduce the fraction to be in lowest terms
        Reduce(GCD(Numerator, Denominator));

        // Make it so that the denominator is always positive
        Reduce(Math.Sign(Denominator));

        // Turn num/denom into a proper fraction and add to wholePart appropriately
        WholePart = Numerator / Denominator;
        Numerator %= Denominator;
    }

    override public String ToString() {
        return String.Format("{0} {1}/{2}", WholePart, Numerator, Denominator);
    }
}

样品用法:

csharp> new MixedNumber(1,11,6);     
2 5/6
csharp> new MixedNumber(1,10,6);   
2 2/3
csharp> new MixedNumber(-2,10,6);  
0 -1/3
csharp> new MixedNumber(-1,-10,6); 
-2 -2/3

Answer 2

int num = 11;
int denom = 6;
int unit = 1;
while (num >= denom)
{
  num -= denom;
  unit++;
}

抱歉，我没有完全理解有关跟踪单位值的部分。