Multiplying Fraction Calculator with 3 Fractions

Multiplying 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'); resultDiv.style.color = '#333'; // Reset color for new calculations if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2) || isNaN(num3) || isNaN(den3)) { resultDiv.innerHTML = 'Please enter valid numbers for all numerators and denominators.'; resultDiv.style.color = 'red'; return; } if (den1 === 0 || den2 === 0 || den3 === 0) { resultDiv.innerHTML = 'Denominator cannot be zero. Please enter a non-zero value.'; resultDiv.style.color = 'red'; 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 += '(' + num1 + '/' + den1 + ') × (' + num2 + '/' + den2 + ') × (' + num3 + '/' + den3 + ') = '; resultHTML += productNumerator + '/' + productDenominator + "; if (simplifiedDenominator === 1) { resultHTML += 'Simplified Result: ' + simplifiedNumerator + ''; } else { resultHTML += 'Simplified Result: ' + simplifiedNumerator + '/' + simplifiedDenominator + ''; } resultDiv.innerHTML = resultHTML; }

Understanding How to Multiply Three Fractions

Multiplying fractions is a fundamental operation in mathematics, and it's surprisingly straightforward, even when dealing with three or more fractions. This calculator helps you quickly find the product of three fractions and simplifies the result for you.

The Basics of Fraction Multiplication

When you multiply fractions, you don't need to find a common denominator, unlike addition or subtraction. The process is much simpler:

1. Multiply the Numerators: Multiply all the top numbers (numerators) together. This product will be the numerator of your answer.
2. Multiply the Denominators: Multiply all the bottom numbers (denominators) together. This product will be the denominator of your answer.
3. Simplify the Result: After multiplying, you'll often get a fraction that can be simplified. To simplify, find the greatest common divisor (GCD) of the new numerator and denominator, and then divide both by the GCD.

Step-by-Step Example

Let's multiply the fractions: (1/2), (3/4), and (2/3).

Step 1: Multiply the Numerators

1 × 3 × 2 = 6

So, the new numerator is 6.

Step 2: Multiply the Denominators

2 × 4 × 3 = 24

So, the new denominator is 24.

This gives us the product: 6/24.

Step 3: Simplify the Result

Now we need to simplify 6/24. We look for the greatest common divisor (GCD) of 6 and 24. The GCD of 6 and 24 is 6.

• Divide the numerator by the GCD: 6 ÷ 6 = 1
• Divide the denominator by the GCD: 24 ÷ 6 = 4

The simplified product is 1/4.

Why is this useful?

Multiplying fractions is essential in various real-world scenarios, from cooking (scaling recipes) and construction (calculating material needs) to finance and engineering. Understanding this concept helps build a strong foundation in mathematics and problem-solving.

Use the calculator above to practice multiplying different sets of three fractions and see their simplified results instantly!