两个分数的加减乘除

两个分数的加减乘除

第一步： 先定义一个分数的类

#import "Fraction.h"

@implementation Fraction
 
//初始化
- (id)initWithFenzi:(NSInteger)fenzi withFenmu:(NSInteger)fenmu{
    self = [super init];
    if (self) {
        _fenzi = fenzi;
        _fenmu = fenmu;
    }
    return self;
}

//便利构造器
+ (id)fractionWithFenzi:(NSInteger)fenzi withFenmu:(NSInteger)fenmu{
    Fraction *num = [[Fraction alloc]initWithFenzi:fenzi withFenmu:fenmu];
    return num;
    
}

第二步：对分子分母进行约分

//最大公约数
- (NSInteger)greatestCommonDivisorWithOneNum:(NSInteger)oneNum andAnotherNumber:(NSInteger)anotherNum{
    
    while (anotherNum != 0) {
        NSInteger temp = oneNum % anotherNum;
        oneNum = anotherNum;
        anotherNum = temp;
    }
    return oneNum;
}
//约分
- (void)reductionOfFraction{
   NSInteger temp = [self greatestCommonDivisorWithOneNum:_fenzi andAnotherNumber:_fenmu];<span style="color:#990000;">//self指代的是调用这个函数的分数，也就是谁
调用这个函数，self指代的就是谁</span>
    _fenzi = _fenzi / temp;
    _fenmu = _fenmu / temp;
}

第三步：进行加减乘除

传入两个分数类型的数，先进行约分，变成最简分数再进行加减乘除，再约分

或者先对两个分数进行加减乘除，再对最后的结果进行约分

加减乘除注意的是：加减法要先通分，乘法直接分子与分子相乘，分母与分母相乘，除法是被除数的分子与除数的分母相乘，被除数的分母与除数的分子相乘

+ (Fraction *)addWithAFraction:(Fraction *)aFraction withBFraction:(Fraction *)bFraction{
    Fraction *add = [[Fraction alloc]init];
    add.fenzi = aFraction.fenzi * bFraction.fenmu + aFraction.fenmu * bFraction.fenzi;
    add.fenmu = aFraction.fenmu * bFraction.fenmu;
    [add reductionOfFraction];
    return add;
    
}
+ (Fraction *)subWithAFraction:(Fraction *)aFraction withBFraction:(Fraction *)bFraction{
    Fraction *sub = [[Fraction alloc]init];
    sub.fenzi = aFraction.fenzi * bFraction.fenmu - aFraction.fenmu * bFraction.fenzi;
    sub.fenmu = aFraction.fenmu * bFraction.fenmu;
    [sub reductionOfFraction];
    return sub;
}

+ (Fraction *)multWithAFraction:(Fraction *)aFraction withBFraction:(Fraction *)bFraction{
    Fraction *mult = [[Fraction alloc]init];
    mult.fenzi = aFraction.fenzi * bFraction.fenzi;
    mult.fenmu = aFraction.fenmu * bFraction.fenmu;
    [mult reductionOfFraction];
    return mult;
}

+ (Fraction *)devidWithAFraction:(Fraction *)aFraction withBFraction:(Fraction *)bFraction{
    Fraction *devid = [[Fraction alloc]init];
    devid.fenzi = aFraction.fenzi * bFraction.fenmu;
    devid.fenmu = aFraction.fenmu * bFraction.fenzi;
    [devid reductionOfFraction];
    return devid;
}

第四步：输出函数

- (void)print{
    NSLog(@"约分后的分数是%ld/%ld", _fenzi, _fenmu);
}