分数的约分及加减乘除运算

定义⼀个分数类（Fraction）
实例变量：分子，分母
⽅法：初始化⽅方法（2个参数），便利构造器，约分，打印，加，减，乘，除。

main.m

#import
#import "Fraction.h"
int main(int argc, const char * argv[]) {
    Fraction *num1 = [Fraction fractionWithNumerator:2 denominator:8];
    [num1 print];
    [num1 reductionOfFraction];
    [num1 print];
    Fraction *num2 = [Fraction fractionWithNumerator:6 denominator:15];
    [num2 print];
    [num2 reductionOfFraction];
    [num2 print];
    Fraction *result = [Fraction minusWitfAFraction:num1 bFraction:num2];
    [result print];
    Fraction *result2 = [Fraction addWitfAFraction:num1 bFraction:num2];
    [result2 print];
    Fraction *result3 = [Fraction timeWitfAFraction:num1 bFraction:num2];
    [result3 print];
    Fraction *result4 = [Fraction divideWitfAFraction:num1 bFraction:num2];
    [result4 print]; 
    return 0;
}

Fraction.h

#import

@interface Fraction : NSObject
{
    NSInteger numerator;//分子
    NSInteger denominator;//分母
}
//自定义初始化方法
- (id)initWithNumerator:(NSInteger)aNumerator;
- (id)initWithNumerator:(NSInteger)aNumerator denominator:(NSInteger)aDenominator;
//便利构造器
+ (Fraction *)fractionWithNumerator:(NSInteger)aNumerator denominator:(NSInteger)aDenominator;

//setter和getter
- (void)setNumerator:(NSInteger)aNumerator;
- (NSInteger)numerator;
- (void)setDenominator:(NSInteger)aDenominator;
- (NSInteger)denominator;

//最大公约数:辗转相除法
- (NSInteger)greatestCommonDivisorWithOneNumber:(NSInteger)oneNumber anotherNumber:(NSInteger)anotherNumber;
//约分
- (void)reductionOfFraction;
//打印
- (void)print;
//加
+ (Fraction *)addWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction;
//减
+ (Fraction *)minusWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction;
//乘
+ (Fraction *)timeWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction;
//除
+ (Fraction *)divideWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction;
@end

Fraction.m

#import "Fraction.h"

@implementation Fraction
- (id)init {
    if (self = [super init]) {
        numerator = 5;
        denominator = 9;
    }
    return self;
}

- (id)initWithNumerator:(NSInteger)aNumerator {
    self = [self init];
    numerator = aNumerator;
    return self;
}
- (id)initWithNumerator:(NSInteger)aNumerator denominator:(NSInteger)aDenominator {
    self = [self initWithNumerator:aNumerator];
    denominator = aDenominator;
    return self;
}

+ (Fraction *)fractionWithNumerator:(NSInteger)aNumerator denominator:(NSInteger)aDenominator {
    return [[Fraction alloc] initWithNumerator:aNumerator denominator:aDenominator];
}

- (void)setNumerator:(NSInteger)aNumerator {
    numerator = aNumerator;
}
- (NSInteger)numerator {
    return numerator;
}
- (void)setDenominator:(NSInteger)aDenominator {
    denominator = aDenominator;
}
- (NSInteger)denominator {
    return denominator;
}
//最大公约数:辗转相除法
- (NSInteger)greatestCommonDivisorWithOneNumber:(NSInteger)oneNumber anotherNumber:(NSInteger)anotherNumber {
    while (anotherNumber != 0) {
        NSInteger temp = oneNumber % anotherNumber;
        oneNumber = anotherNumber;
        anotherNumber = temp;
    }
    return oneNumber;
}

//约分
- (void)reductionOfFraction {
    NSInteger temp = [self greatestCommonDivisorWithOneNumber:numerator anotherNumber:denominator];
    numerator /= temp;
    denominator /= temp;
}

//打印
- (void)print {
    NSLog(@"这个分数是%ld / %ld", numerator, denominator);
}

//加
+ (Fraction *)addWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction {
    Fraction *result = [[Fraction alloc] init];
    result.denominator = aFraction.denominator * bFraction.denominator;
    result.numerator = aFraction.numerator * bFraction.denominator + bFraction.numerator * aFraction.denominator;
    [result reductionOfFraction];
    return result;
}
//减
+ (Fraction *)minusWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction {
    //存储结构
    Fraction *result = [[Fraction alloc] init];
    //分母
    result.denominator = aFraction.denominator * bFraction.denominator;
    //分子
    result.numerator = aFraction.numerator * bFraction.denominator - bFraction.numerator * aFraction.denominator;
    //约分
    [result reductionOfFraction];
    return result;
}

//乘
+ (Fraction *)timeWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction {
    Fraction *result = [[Fraction alloc] init];
    result.denominator = aFraction.denominator * bFraction.denominator;
    result.numerator = aFraction.numerator * bFraction.numerator;
    [result reductionOfFraction];
    return result;
}
//除
+ (Fraction *)divideWitfAFraction:(Fraction *)aFraction bFraction:(Fraction *)bFraction {
    Fraction *result = [[Fraction alloc] init];
    result.denominator = aFraction.denominator * bFraction.numerator;
    result.numerator = aFraction.numerator * bFraction.denominator;
    [result reductionOfFraction];
    return result;
}
@end