common denominator
时间: 2023-11-15 16:06:15 浏览: 20
A common denominator is a shared multiple of the denominators of two or more fractions. In other words, it is the smallest number that each denominator can divide into evenly. For example, the common denominator of the fractions 1/3 and 1/4 is 12, because both 3 and 4 can divide into 12 evenly. When fractions have a common denominator, they can be easily added or subtracted.
相关问题
Create a class called Rational for performing arithmetic with fractions. Use integer variables to represent the private data of the class – the numerator and the denominator. Provide a constructor that enables an object of this class to be initialized when it’s declared. The constructor should store the fraction in reduced form. For example, the fraction 2/4 would be stored in the object as 1 in the numerator and 2 in the denominator. In order to compute the reduced form, you need to write a reduction function which uses the Euclidean algorithm to get the greatest common divisor (GCD) of the numerator and denominator first and then divides GCD to get the reduced numerator and denominator. Provide public member functions that perform each of the following tasks: (a) Subtract a Rational number from the other Rational number. The result should be stored in reduced form. (b) Divide a Rational number by the other Rational number. The result should be stored in reduced form. (c) Print Rational numbers in the form a/b, where a is the numerator and b is the denominator. (d)Compare two Rational numbers to make sure which one is smaller or they are equal. (1 for the first number, 2 for the second number and 0 if they are equal) Please also write a main function to prompt the user to input two Rational numbers . Subtract one number from the other from these two numbers using (a) and then print the result using (c). Divide one number from the other from these two numbers using (b) and then print the result using (c). Compare these two Rational numbers using (d) and indicate which one is smaller or they are equal. 用c++5.11寫出,且使用using namespace std;
以下是符合要求的C++ 代码:
```
#include <iostream>
using namespace std;
class Rational {
private:
int numerator, denominator;
int gcd(int a, int b) {
if (b == 0) return a;
return gcd(b, a % b);
}
public:
Rational(int num = 0, int den = 1) {
int divisor = gcd(num, den);
numerator = num / divisor;
denominator = den / divisor;
}
Rational operator- (Rational other) {
int num = numerator * other.denominator - other.numerator * denominator;
int den = denominator * other.denominator;
return Rational(num, den);
}
Rational operator/ (Rational other) {
int num = numerator * other.denominator;
int den = denominator * other.numerator;
return Rational(num, den);
}
void print() {
cout << numerator << "/" << denominator;
}
int compare(Rational other) {
int num1 = numerator * other.denominator;
int num2 = other.numerator * denominator;
if (num1 < num2) return 1;
if (num1 > num2) return 2;
return 0;
}
};
int main() {
Rational r1, r2;
cout << "Enter the first rational number (numerator denominator): ";
cin >> r1;
cout << "Enter the second rational number (numerator denominator): ";
cin >> r2;
Rational diff = r1 - r2;
cout << "The difference is ";
diff.print();
cout << endl;
Rational quotient = r1 / r2;
cout << "The quotient is ";
quotient.print();
cout << endl;
int result = r1.compare(r2);
if (result == 1) {
cout << "The first number is smaller." << endl;
} else if (result == 2) {
cout << "The second number is smaller." << endl;
} else {
cout << "The two numbers are equal." << endl;
}
return 0;
}
```
请注意,此代码使用了重载运算符-和/来实现两个Rational数的减法和除法。此外,它还定义了一个比较函数来比较两个Rational数的大小。在主函数中,我们首先提示用户输入两个Rational数,然后执行所需的操作并输出结果。
1/3+3/5+5/7 java
To add the fractions 1/3, 3/5, and 5/7 in Java, you can use the following code:
```
int num1 = 1;
int den1 = 3;
int num2 = 3;
int den2 = 5;
int num3 = 5;
int den3 = 7;
int lcm1 = den1 * den2 / gcd(den1, den2);
int lcm2 = lcm1 * den3 / gcd(lcm1, den3);
int newNum1 = num1 * lcm1 / den1;
int newNum2 = num2 * lcm1 / den2;
int newNum3 = num3 * lcm2 / den3;
int sumNum = newNum1 + newNum2 + newNum3;
int sumDen = lcm2;
int gcd = gcd(sumNum, sumDen);
int finalNum = sumNum / gcd;
int finalDen = sumDen / gcd;
System.out.println(finalNum + "/" + finalDen);
```
This code first defines the fractions as separate numerators and denominators. It then calculates the least common multiple (LCM) of the denominators using a helper function called `gcd` to calculate the greatest common divisor (GCD) between two numbers. It then converts each fraction to have a common denominator and adds them together. Finally, it simplifies the resulting fraction by dividing both the numerator and denominator by their GCD and prints the result.
相关推荐
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![.zip](https://img-home.csdnimg.cn/images/20210720083646.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)