Adding Unlike Fractions Calculator

Adding Unlike Fractions Calculator

// Function to calculate the Greatest Common Divisor (GCD) 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 to calculate the Least Common Multiple (LCM) function lcm(a, b) { if (a === 0 || b === 0) return 0; return Math.abs(a * b) / gcd(a, b); } function calculateFractionSum() { var numerator1 = parseFloat(document.getElementById('numerator1').value); var denominator1 = parseFloat(document.getElementById('denominator1').value); var numerator2 = parseFloat(document.getElementById('numerator2').value); var denominator2 = parseFloat(document.getElementById('denominator2').value); var resultDiv = document.getElementById('result'); // Input validation if (isNaN(numerator1) || isNaN(denominator1) || isNaN(numerator2) || isNaN(denominator2)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (denominator1 === 0 || denominator2 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; return; } if (denominator1 < 0 || denominator2 < 0) { resultDiv.innerHTML = "Denominators should be positive. Please adjust your input."; return; } if (!Number.isInteger(numerator1) || !Number.isInteger(denominator1) || !Number.isInteger(numerator2) || !Number.isInteger(denominator2)) { resultDiv.innerHTML = "Please enter whole numbers for numerators and denominators."; return; } // Find the Least Common Multiple (LCM) of the denominators var commonDenominator = lcm(denominator1, denominator2); // Convert fractions to equivalent fractions with the common denominator var newNumerator1 = numerator1 * (commonDenominator / denominator1); var newNumerator2 = numerator2 * (commonDenominator / denominator2); // Add the numerators var sumNumerator = newNumerator1 + newNumerator2; // Simplify the resulting fraction var commonDivisor = gcd(sumNumerator, commonDenominator); var simplifiedNumerator = sumNumerator / commonDivisor; var simplifiedDenominator = commonDenominator / commonDivisor; // Display the result if (simplifiedDenominator === 1) { resultDiv.innerHTML = "The sum is: " + simplifiedNumerator + ""; } else { resultDiv.innerHTML = "The sum is: " + simplifiedNumerator + "/" + simplifiedDenominator + ""; } } // Calculate on load with default values window.onload = calculateFractionSum;

Understanding Unlike Fractions

Unlike fractions are fractions that have different denominators. For example, 1/2 and 1/3 are unlike fractions because their denominators (2 and 3) are not the same. Adding or subtracting unlike fractions requires an extra step compared to like fractions: you must first find a common denominator.

Why a Common Denominator is Essential

Imagine you have half a pizza and a third of a different pizza. To know the total amount of pizza you have, you can't just add the numerators (1+1) because the 'units' (halves vs. thirds) are different. You need to express both amounts in terms of the same unit, like sixths. Once both fractions refer to the same size pieces, you can easily combine them.

Steps to Add Unlike Fractions

1. Find the Least Common Multiple (LCM) of the Denominators: The LCM is the smallest positive integer that is a multiple of both denominators. This will be your new common denominator.
2. Convert Each Fraction to an Equivalent Fraction: For each fraction, multiply both its numerator and denominator by the factor that makes its denominator equal to the LCM. This ensures the value of the fraction remains unchanged.
3. Add the Numerators: Once both fractions have the same denominator, you can simply add their numerators. The denominator remains the common denominator.
4. Simplify the Resulting Fraction: If possible, simplify the sum by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). This reduces the fraction to its simplest form.

Example Calculation

Let's add 1/4 and 2/5 using the steps above:

1. Find the LCM of 4 and 5: The multiples of 4 are 4, 8, 12, 16, 20, 24… The multiples of 5 are 5, 10, 15, 20, 25… The LCM is 20.
2. Convert to Equivalent Fractions:
   • For 1/4: To get a denominator of 20, we multiply 4 by 5. So, we multiply the numerator by 5 as well: (1 * 5) / (4 * 5) = 5/20.
   • For 2/5: To get a denominator of 20, we multiply 5 by 4. So, we multiply the numerator by 4 as well: (2 * 4) / (5 * 4) = 8/20.
3. Add the Numerators: Now we add the new numerators: 5/20 + 8/20 = (5 + 8) / 20 = 13/20.
4. Simplify the Result: The fraction 13/20 cannot be simplified further because 13 is a prime number and 20 is not a multiple of 13.

So, 1/4 + 2/5 = 13/20.

This calculator automates these steps, allowing you to quickly find the sum of any two unlike fractions.