3 Fraction Calculator

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3 Fraction Calculator

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+ – * /
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+ – * /
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Result will appear here.
function gcd(a, b) { return b === 0 ? a : gcd(b, a % b); } function simplifyFraction(fraction) { if (fraction.numerator === 0) { return { numerator: 0, denominator: 1 }; } var common = gcd(Math.abs(fraction.numerator), Math.abs(fraction.denominator)); var sign = (fraction.numerator 0) || (fraction.numerator > 0 && fraction.denominator < 0) ? -1 : 1; return { numerator: sign * (Math.abs(fraction.numerator) / common), denominator: Math.abs(fraction.denominator) / common }; } function addFractions(f1, f2) { return { numerator: f1.numerator * f2.denominator + f2.numerator * f1.denominator, denominator: f1.denominator * f2.denominator }; } function subtractFractions(f1, f2) { return { numerator: f1.numerator * f2.denominator – f2.numerator * f1.denominator, denominator: f1.denominator * f2.denominator }; } function multiplyFractions(f1, f2) { return { numerator: f1.numerator * f2.numerator, denominator: f1.denominator * f2.denominator }; } function divideFractions(f1, f2) { if (f2.numerator === 0) { return null; // Division by zero } return { numerator: f1.numerator * f2.denominator, denominator: f1.denominator * f2.numerator }; } function calculateFractions() { var num1 = parseFloat(document.getElementById('num1').value); var den1 = parseFloat(document.getElementById('den1').value); var num2 = parseFloat(document.getElementById('num2').value); var den2 = parseFloat(document.getElementById('den2').value); var num3 = parseFloat(document.getElementById('num3').value); var den3 = parseFloat(document.getElementById('den3').value); var operation1 = document.getElementById('operation1').value; var operation2 = document.getElementById('operation2').value; var resultDiv = document.getElementById('fractionResult'); if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2) || isNaN(num3) || isNaN(den3)) { resultDiv.innerHTML = "Please enter valid numbers for all numerators and denominators."; return; } if (den1 === 0 || den2 === 0 || den3 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; return; } var fraction1 = { numerator: num1, denominator: den1 }; var fraction2 = { numerator: num2, denominator: den2 }; var fraction3 = { numerator: num3, denominator: den3 }; var intermediateResult; // Perform first operation switch (operation1) { case 'add': intermediateResult = addFractions(fraction1, fraction2); break; case 'subtract': intermediateResult = subtractFractions(fraction1, fraction2); break; case 'multiply': intermediateResult = multiplyFractions(fraction1, fraction2); break; case 'divide': intermediateResult = divideFractions(fraction1, fraction2); if (intermediateResult === null) { resultDiv.innerHTML = "Cannot divide by zero (Fraction 2 is zero)."; return; } break; } // Perform second operation var finalResult; switch (operation2) { case 'add': finalResult = addFractions(intermediateResult, fraction3); break; case 'subtract': finalResult = subtractFractions(intermediateResult, fraction3); break; case 'multiply': finalResult = multiplyFractions(intermediateResult, fraction3); break; case 'divide': finalResult = divideFractions(intermediateResult, fraction3); if (finalResult === null) { resultDiv.innerHTML = "Cannot divide by zero (Fraction 3 is zero)."; return; } break; } var simplified = simplifyFraction(finalResult); if (simplified.denominator === 1) { resultDiv.innerHTML = "Result: " + simplified.numerator; } else { resultDiv.innerHTML = "Result: " + simplified.numerator + " / " + simplified.denominator; } }

Understanding the 3 Fraction Calculator

Our 3 Fraction Calculator is a versatile tool designed to help you perform arithmetic operations on three fractions sequentially. Whether you need to add, subtract, multiply, or divide, this calculator simplifies complex fraction problems into easy-to-understand steps, providing you with the simplified result.

What is a Fraction?

A fraction represents a part of a whole. It consists of two main parts:

  • Numerator: The top number, indicating how many parts of the whole are being considered.
  • Denominator: The bottom number, indicating the total number of equal parts the whole is divided into.
For example, in the fraction 1/2, '1' is the numerator and '2' is the denominator, meaning one out of two equal parts.

How to Use the Calculator

  1. Enter Fractions: Input the numerator and denominator for each of the three fractions in their respective fields.
  2. Select Operations: Choose the desired operation (addition, subtraction, multiplication, or division) for 'Operation 1' (between Fraction 1 and Fraction 2) and 'Operation 2' (between the result of the first operation and Fraction 3).
  3. Calculate: Click the "Calculate" button to see the simplified result.

Fraction Operations Explained

1. Adding Fractions

To add fractions, they must have a common denominator. If they don't, you'll need to find the least common multiple (LCM) of the denominators and convert the fractions. Once they have the same denominator, you simply add the numerators and keep the denominator the same.
Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

2. Subtracting Fractions

Similar to addition, fractions must have a common denominator for subtraction. Find the LCM if necessary, convert the fractions, then subtract the numerators while keeping the denominator.
Example: 1/2 – 1/3 = 3/6 – 2/6 = 1/6

3. Multiplying Fractions

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together.
Example: 1/2 * 1/3 = (1*1) / (2*3) = 1/6

4. Dividing Fractions

To divide fractions, you "keep, change, flip." Keep the first fraction as it is, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction. Then, multiply as usual.
Example: 1/2 / 1/3 = 1/2 * 3/1 = (1*3) / (2*1) = 3/2

Simplifying Fractions

After performing operations, the result is often an unsimplified fraction. Simplifying means reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, 2/4 simplifies to 1/2 because the GCD of 2 and 4 is 2. Our calculator automatically simplifies the final result for you.

Examples Using the Calculator

Example 1: Addition of three fractions

  • Fraction 1: 1/2
  • Operation 1: +
  • Fraction 2: 1/3
  • Operation 2: +
  • Fraction 3: 1/4
  • Calculation: (1/2 + 1/3) + 1/4 = (3/6 + 2/6) + 1/4 = 5/6 + 1/4 = 10/12 + 3/12 = 13/12
  • Calculator Result: 13 / 12

Example 2: Mixed Operations

  • Fraction 1: 3/4
  • Operation 1: *
  • Fraction 2: 2/5
  • Operation 2: –
  • Fraction 3: 1/10
  • Calculation: (3/4 * 2/5) – 1/10 = 6/20 – 1/10 = 3/10 – 1/10 = 2/10 = 1/5
  • Calculator Result: 1 / 5

Example 3: Division and Addition

  • Fraction 1: 1/2
  • Operation 1: /
  • Fraction 2: 1/4
  • Operation 2: +
  • Fraction 3: 1/3
  • Calculation: (1/2 / 1/4) + 1/3 = (1/2 * 4/1) + 1/3 = 4/2 + 1/3 = 2 + 1/3 = 6/3 + 1/3 = 7/3
  • Calculator Result: 7 / 3

This 3 Fraction Calculator is an invaluable tool for students, educators, and anyone needing to quickly and accurately perform operations on multiple fractions. It handles the complexities of common denominators, reciprocals, and simplification, allowing you to focus on understanding the concepts.

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