Converting a proper fraction to mixed fraction - JavaScript

A proper fraction is one where the numerator is smaller than the denominator, represented in p/q form where both p and q are natural numbers.

What is a Mixed Fraction?

When we divide the numerator (a) of a fraction by its denominator (b), we get a quotient (q) and remainder (r). The mixed fraction form for fraction a/b is:

This is pronounced as "q wholes and r by b".

Problem Statement

We need to write a JavaScript function that takes an array of two numbers representing a proper fraction and returns an array with three numbers representing its mixed form.

Algorithm

To convert proper fraction to mixed fraction:

• Calculate quotient using Math.floor(numerator / denominator)
• Calculate remainder using numerator % denominator
• If remainder is 0, return only the quotient
• Otherwise, return [quotient, remainder, denominator]

Example

const arr = [43, 13];

const properToMixed = arr => {
    const quotient = Math.floor(arr[0] / arr[1]);
    const remainder = arr[0] % arr[1];
    
    if(remainder === 0) {
        return [quotient];
    } else {
        return [quotient, remainder, arr[1]];
    }
};

console.log(properToMixed(arr));
console.log("43/13 = 3 wholes and 4/13");

[ 3, 4, 13 ]
43/13 = 3 wholes and 4/13

Additional Examples

// Test with different fractions
console.log(properToMixed([17, 5]));   // 17/5 = 3 2/5
console.log(properToMixed([25, 4]));   // 25/4 = 6 1/4
console.log(properToMixed([20, 5]));   // 20/5 = 4 (whole number)

[ 3, 2, 5 ]
[ 6, 1, 4 ]
[ 4 ]

Conclusion

Converting proper fractions to mixed fractions involves simple division to find quotient and remainder. This function handles both cases where the division results in a whole number or leaves a remainder.