Fraction Calculator Three Fractions Multiplying

Three Fraction Multiplication Calculator

function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var temp = b; b = a % b; a = temp; } return a; } function calculateFractionMultiplication() { var num1 = parseFloat(document.getElementById("numerator1").value); var den1 = parseFloat(document.getElementById("denominator1").value); var num2 = parseFloat(document.getElementById("numerator2").value); var den2 = parseFloat(document.getElementById("denominator2").value); var num3 = parseFloat(document.getElementById("numerator3").value); var den3 = parseFloat(document.getElementById("denominator3").value); var resultFractionElement = document.getElementById("resultFraction"); var simplifiedFractionElement = document.getElementById("simplifiedFraction"); if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2) || isNaN(num3) || isNaN(den3)) { resultFractionElement.innerHTML = "Product: Please enter valid numbers for all fields."; simplifiedFractionElement.innerHTML = "Simplified Product: -"; return; } if (den1 === 0 || den2 === 0 || den3 === 0) { resultFractionElement.innerHTML = "Product: Denominators cannot be zero."; simplifiedFractionElement.innerHTML = "Simplified Product: -"; return; } var productNumerator = num1 * num2 * num3; var productDenominator = den1 * den2 * den3; resultFractionElement.innerHTML = "Product: " + productNumerator + " / " + productDenominator; var commonDivisor = gcd(productNumerator, productDenominator); var simplifiedNumerator = productNumerator / commonDivisor; var simplifiedDenominator = productDenominator / commonDivisor; simplifiedFractionElement.innerHTML = "Simplified Product: " + simplifiedNumerator + " / " + simplifiedDenominator; }

Understanding Three Fraction Multiplication

Multiplying fractions is a fundamental operation in mathematics, and extending it to three fractions follows a straightforward rule. Unlike addition or subtraction, you don't need a common denominator to multiply fractions. This makes the process relatively simple and direct.

How to Multiply Three Fractions

To multiply three fractions, you simply follow two main steps:

1. Multiply all the numerators together: The numerator of the product fraction will be the result of multiplying the numerators of all three individual fractions.
2. Multiply all the denominators together: Similarly, the denominator of the product fraction will be the result of multiplying the denominators of all three individual fractions.

The resulting fraction is the product of the three fractions. After obtaining the product, it's good practice to simplify the fraction to its lowest terms.

Simplifying the Product

Simplifying a fraction means dividing both its numerator and denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Simplifying fractions makes them easier to understand and work with.

Example Calculation

Let's multiply the following three fractions: (1/2) * (3/4) * (5/6)

1. Multiply the numerators:
   1 * 3 * 5 = 15
2. Multiply the denominators:
   2 * 4 * 6 = 48
3. The product fraction is:
   15/48
4. Simplify the fraction:
   Find the Greatest Common Divisor (GCD) of 15 and 48. The GCD of 15 and 48 is 3.
   Divide both the numerator and the denominator by 3:
   15 ÷ 3 = 5
   48 ÷ 3 = 16
   The simplified product is 5/16.

Using the Calculator

Our Three Fraction Multiplication Calculator makes this process effortless. Simply enter the numerator and denominator for each of the three fractions into the respective input fields. Click the "Calculate Product" button, and the calculator will instantly display both the unsimplified product and the simplified product, saving you time and ensuring accuracy.