How to implement reduction in javascript

Javascript is a widely used programming language that can be used to develop various web, mobile and desktop applications. When writing Javascript code, you often need to perform operations and calculations on numbers, and these numbers often need to be reduced. How can we implement reduction in Javascript? Below, we will discuss them one by one.

1. What is reduction

In mathematics, reduction is to write a fraction into another equivalent fraction. The numerator and denominator are divided by two numbers that are divisible. The quotient is called a fraction.

For example: $\frac{10}{20}$ can be reduced to $\frac{1}{2}$, $\frac{20}{25}$ can be reduced to $\ frac{4}{5}$.

2. Introduction to the reduction method

1. Find the greatest common divisor method

Find the greatest common divisor of the numerator and denominator, and then divide the numerator and denominator by the greatest common divisor at the same time. .

The code is as follows:

function gcd(a, b) {
    if (b === 0) {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

function reduceFraction(numerator, denominator) {
    var divisor = gcd(numerator, denominator);
    return [numerator / divisor, denominator / divisor];
}

For example: for the fraction $\frac{24}{60}$, find the greatest common divisor to be $12$, then the final approximation is $2/5$ .

2. Circular division method

Divide the numerator and denominator by an integer greater than $1$ at the same time until the numerator and denominator have no common divisors, then you can get the reduced fraction.

The code is as follows:

function reduceFraction(numerator, denominator) {
    var gcd = 1;
    var smaller = Math.min(numerator, denominator);
    for (var i = 2; i <= smaller; i++) {
        if (numerator % i === 0 && denominator % i === 0) {
            gcd = i;
        }
    }
    return [numerator / gcd, denominator / gcd];
}

For example: for the fraction $\frac{24}{60}$, you can first divide it by $2$ to get $\frac{12}{30 }$, and then divide it by $2$ to get $\frac{6}{15}$, and finally divide it into $2/5$.

3. Subtraction method

Subtract the same number from the numerator and denominator at the same time until the numerator and denominator have no common divisors, then you can get the reduced fraction.

The code is as follows:

function reduceFraction(numerator, denominator) {
    var smaller = Math.min(numerator, denominator);
    for (var i = smaller; i >= 2; i--) {
        if (numerator % i === 0 && denominator % i === 0) {
            numerator /= i;
            denominator /= i;
        }
    }
    return [numerator, denominator];
}

For example: for the fraction $\frac{24}{60}$, you can first subtract $12$ from its numerator and denominator at the same time to get $\frac{2 }{5}$, and finally got about $2/5$.

3. Conclusion

There are many ways to reduce fractions in Javascript, and we can choose according to our own preferences and needs. I hope this article can help everyone learn and understand the reduction method.

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