Enter the numerators and denominators for the two fractions you want to subtract.
Understanding Fraction Subtraction
Subtracting fractions is a fundamental arithmetic operation that involves finding the difference between two fractional quantities. Like adding fractions, the key principle is that the fractions must have a common denominator before their numerators can be subtracted.
The Process:
Find a Common Denominator: If the fractions don't share the same denominator, you need to find a common denominator. The easiest way is often to multiply the two denominators together. A more efficient method is to find the Least Common Multiple (LCM) of the denominators.
Convert Fractions: Once you have a common denominator, convert each fraction to an equivalent fraction with that new denominator. To do this, multiply the numerator and denominator of each fraction by the same number (the number needed to turn its original denominator into the common denominator).
Subtract the Numerators: With a common denominator, subtract the numerator of the second fraction from the numerator of the first fraction.
Keep the Denominator: The denominator of the resulting fraction remains the common denominator found in step 1.
Simplify (Optional but Recommended): Reduce the resulting fraction to its simplest form by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD).
Example Calculation:
Let's subtract 1/3 from 1/2 using our calculator's logic:
Fraction 1:1/2 (Numerator = 1, Denominator = 2)
Fraction 2:1/3 (Numerator = 1, Denominator = 3)
Common Denominator: The LCM of 2 and 3 is 6.
Convert Fractions:
1/2 becomes (1*3)/(2*3) = 3/6
1/3 becomes (1*2)/(3*2) = 2/6
Subtract Numerators:3 - 2 = 1
Keep Denominator: The denominator is 6.
Result: The difference is 1/6.
This calculator automates these steps for you, providing quick and accurate results for any two fractions.
function gcd(a, b) {
var a = Math.abs(a);
var b = Math.abs(b);
while (b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function simplifyFraction(num, den) {
if (den === 0) return { num: NaN, den: NaN };
if (num === 0) return { num: 0, den: 1 };
var commonDivisor = gcd(num, den);
num = num / commonDivisor;
den = den / commonDivisor;
if (den < 0) {
num = -num;
den = -den;
}
return { num: num, den: den };
}
function subtractFractions() {
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 resultDisplay = document.getElementById("result");
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDisplay.textContent = "Please enter valid numbers.";
resultDisplay.style.color = "red";
resultDisplay.style.borderColor = "red";
return;
}
if (den1 === 0 || den2 === 0) {
resultDisplay.textContent = "Denominators cannot be zero.";
resultDisplay.style.color = "red";
resultDisplay.style.borderColor = "red";
return;
}
// Calculate common denominator (LCM method)
var commonDenominator = (den1 * den2) / gcd(den1, den2);
// Convert numerators to equivalent fractions
var newNum1 = num1 * (commonDenominator / den1);
var newNum2 = num2 * (commonDenominator / den2);
// Subtract numerators
var resultNum = newNum1 – newNum2;
var resultDen = commonDenominator;
// Simplify the result
var simplified = simplifyFraction(resultNum, resultDen);
if (isNaN(simplified.num) || isNaN(simplified.den)) {
resultDisplay.textContent = "Calculation error.";
resultDisplay.style.color = "red";
resultDisplay.style.borderColor = "red";
} else if (simplified.den === 1) {
resultDisplay.textContent = simplified.num;
resultDisplay.style.color = "#004a99";
resultDisplay.style.borderColor = "#28a745";
} else {
resultDisplay.textContent = simplified.num + " / " + simplified.den;
resultDisplay.style.color = "#004a99";
resultDisplay.style.borderColor = "#28a745";
}
}