Enter your original fraction and a target value (either a new numerator or a new denominator) to find an equivalent fraction.
New Denominator
New Numerator
Understanding Equivalent Fractions
Equivalent fractions are different fractions that represent the same value or proportion. For example, 1/2, 2/4, 3/6, and 50/100 are all equivalent fractions because they all represent half of a whole. They look different but have the same value.
How to Find Equivalent Fractions
To find an equivalent fraction, you multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. This operation doesn't change the value of the fraction, only its appearance.
Multiplying: If you have 1/3 and you want an equivalent fraction with a denominator of 9, you'd multiply both the numerator and denominator by 3 (since 3 * 3 = 9). So, (1 * 3) / (3 * 3) = 3/9.
Dividing: If you have 6/12 and you want an equivalent fraction with a denominator of 2, you'd divide both the numerator and denominator by 6 (since 12 / 6 = 2). So, (6 / 6) / (12 / 6) = 1/2. This process is also known as simplifying fractions.
Why Are Equivalent Fractions Important?
Equivalent fractions are fundamental in mathematics, especially when:
Comparing Fractions: To compare fractions with different denominators, you often convert them to equivalent fractions with a common denominator.
Adding and Subtracting Fractions: You must have a common denominator to add or subtract fractions. Finding equivalent fractions helps achieve this.
Simplifying Fractions: Reducing a fraction to its simplest form (e.g., 6/12 to 1/2) involves finding an equivalent fraction by dividing by the greatest common divisor.
How to Use This Calculator
Enter Original Numerator: Input the top number of your starting fraction.
Enter Original Denominator: Input the bottom number of your starting fraction.
Enter Target Value: Input the new numerator or new denominator you want for your equivalent fraction.
Select Target Value Is: Choose whether the "Target Value" you entered is a "New Denominator" or a "New Numerator".
Click "Calculate Equivalent Fraction": The calculator will then display the equivalent fraction.
Examples
Example 1: Find an equivalent fraction for 1/2 with a new denominator of 10.
Original Numerator: 1
Original Denominator: 2
Target Value: 10
Target Value Is: New Denominator
Result: 5/10
Example 2: Find an equivalent fraction for 3/4 with a new numerator of 9.
Original Numerator: 3
Original Denominator: 4
Target Value: 9
Target Value Is: New Numerator
Result: 9/12
Example 3: Find an equivalent fraction for 6/8 with a new denominator of 4.
Original Numerator: 6
Original Denominator: 8
Target Value: 4
Target Value Is: New Denominator
Result: 3/4
function calculateEquivalentFraction() {
var originalNumerator = parseFloat(document.getElementById("originalNumerator").value);
var originalDenominator = parseFloat(document.getElementById("originalDenominator").value);
var targetValue = parseFloat(document.getElementById("targetValue").value);
var targetType = document.getElementById("targetType").value;
var resultDiv = document.getElementById("equivalentFractionResult");
// Input validation
if (isNaN(originalNumerator) || isNaN(originalDenominator) || isNaN(targetValue)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (originalDenominator === 0) {
resultDiv.innerHTML = "Original Denominator cannot be zero.";
return;
}
if (targetValue === 0 && targetType === "denominator") {
resultDiv.innerHTML = "Target Denominator cannot be zero.";
return;
}
if (targetValue === 0 && targetType === "numerator" && originalNumerator !== 0) {
// If target numerator is 0, and original numerator is not 0, then the new denominator would be 0, which is invalid.
// If original numerator is 0, then 0/originalDenominator = 0/newDenominator, so 0/any_non_zero_number is valid.
// This case is handled by the originalNumerator === 0 check below.
}
var newNumerator;
var newDenominator;
if (targetType === "denominator") {
// We have originalNumerator/originalDenominator and targetDenominator
// We need to find newNumerator such that newNumerator/targetDenominator = originalNumerator/originalDenominator
// newNumerator = (originalNumerator / originalDenominator) * targetDenominator
newNumerator = (originalNumerator / originalDenominator) * targetValue;
newDenominator = targetValue;
resultDiv.innerHTML = "The equivalent fraction is: " + newNumerator.toFixed(4).replace(/\.?0+$/, "") + " / " + newDenominator.toFixed(4).replace(/\.?0+$/, "") + "";
} else if (targetType === "numerator") {
// We have originalNumerator/originalDenominator and targetNumerator
// We need to find newDenominator such that targetNumerator/newDenominator = originalNumerator/originalDenominator
// newDenominator = (originalDenominator / originalNumerator) * targetNumerator
if (originalNumerator === 0 && targetValue !== 0) {
resultDiv.innerHTML = "If the original numerator is zero, the target numerator must also be zero to form an equivalent fraction.";
return;
}
if (originalNumerator === 0 && targetValue === 0) {
// 0/X = 0/Y, any non-zero Y is valid. Let's just say 0/1 for simplicity or keep original denominator.
newNumerator = 0;
newDenominator = originalDenominator; // Or 1, or targetValue if it was meant to be a multiplier.
resultDiv.innerHTML = "The equivalent fraction is: 0 / " + newDenominator.toFixed(4).replace(/\.?0+$/, "") + "";
return;
}
newDenominator = (originalDenominator / originalNumerator) * targetValue;
newNumerator = targetValue;
resultDiv.innerHTML = "The equivalent fraction is: " + newNumerator.toFixed(4).replace(/\.?0+$/, "") + " / " + newDenominator.toFixed(4).replace(/\.?0+$/, "") + "";
} else {
resultDiv.innerHTML = "An unexpected error occurred. Please try again.";
}
}
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