Multiplication of Three Fractions Calculator

Multiplication of Three Fractions 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 calculateFractions() { 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 resultDiv = document.getElementById('result'); if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2) || isNaN(num3) || isNaN(den3)) { resultDiv.innerHTML = "

Error:

Please enter valid numbers for all numerators and denominators."; return; } if (den1 === 0 || den2 === 0 || den3 === 0) { resultDiv.innerHTML = "

Error:

Denominator cannot be zero."; return; } var productNumerator = num1 * num2 * num3; var productDenominator = den1 * den2 * den3; var commonDivisor = gcd(productNumerator, productDenominator); var simplifiedNumerator = productNumerator / commonDivisor; var simplifiedDenominator = productDenominator / commonDivisor; var resultHtml = "

Calculation Result:

"; resultHtml += "The product of the three fractions is: " + productNumerator + " / " + productDenominator + ""; if (simplifiedDenominator === 1) { resultHtml += "Which simplifies to: " + simplifiedNumerator + ""; } else { resultHtml += "Which simplifies to: " + simplifiedNumerator + " / " + simplifiedDenominator + ""; } resultDiv.innerHTML = resultHtml; }

Understanding Multiplication of Three Fractions

Multiplying fractions is a fundamental operation in mathematics, and extending it to three or more fractions follows a straightforward process. This calculator helps you quickly find the product of three given fractions, simplifying the result for you.

How to Multiply Fractions

The rule for multiplying fractions is simple: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. This rule applies regardless of how many fractions you are multiplying.

Steps for Three Fractions:

1. Identify Numerators and Denominators: For each fraction, determine its numerator (the top number) and its denominator (the bottom number).
2. Multiply All Numerators: Take the numerators of all three fractions and multiply them together. This product will be the numerator of your answer.
3. Multiply All Denominators: Take the denominators of all three fractions and multiply them together. This product will be the denominator of your answer.
4. Simplify the Result (Optional but Recommended): The resulting fraction can often be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). This makes the fraction easier to understand and work with.

Example Calculation

Let's multiply the following three fractions: ¹⁄₂, ³⁄₄, and ²⁄₅.

1. Numerators: 1, 3, 2
2. Denominators: 2, 4, 5
3. Multiply Numerators: 1 × 3 × 2 = 6
4. Multiply Denominators: 2 × 4 × 5 = 40
5. Resulting Fraction: ⁶⁄₄₀
6. Simplify: The greatest common divisor (GCD) of 6 and 40 is 2.
   • Numerator: 6 ÷ 2 = 3
   • Denominator: 40 ÷ 2 = 20
   The simplified fraction is ³⁄₂₀.

So, ¹⁄₂ × ³⁄₄ × ²⁄₅ = ³⁄₂₀.

Using the Calculator

Our Multiplication of Three Fractions Calculator makes this process effortless:

1. Enter the numerator and denominator for your first fraction in the designated fields.
2. Repeat for the second and third fractions.
3. Click the "Calculate Product" button.
4. The calculator will instantly display both the original product and its simplified form.

This tool is perfect for students, educators, or anyone needing to quickly and accurately multiply fractions without manual calculation errors.