Equivalent Fraction Calculator

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Equivalent Fraction Calculator

Find an equivalent fraction with:

Understanding Equivalent Fractions

Equivalent fractions are different fractions that represent the same value or proportion. For example, 1/2, 2/4, 3/6, and 4/8 are all equivalent fractions because they all represent half of a whole. They look different but have the same mathematical 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.

For instance, to find an equivalent fraction for 1/2 with a denominator of 8:

  • You need to multiply the original denominator (2) by 4 to get the new denominator (8).
  • Therefore, you must also multiply the original numerator (1) by 4.
  • This gives you 1 × 4 = 4 for the new numerator.
  • So, 1/2 is equivalent to 4/8.

Similarly, if you have 6/9 and want to find an equivalent fraction with a numerator of 2:

  • You need to divide the original numerator (6) by 3 to get the new numerator (2).
  • Therefore, you must also divide the original denominator (9) by 3.
  • This gives you 9 ÷ 3 = 3 for the new denominator.
  • So, 6/9 is equivalent to 2/3.

Why are Equivalent Fractions Important?

Equivalent fractions are fundamental in mathematics for several reasons:

  • Simplifying Fractions: They help reduce fractions to their simplest form (e.g., 6/8 simplifies to 3/4).
  • Adding and Subtracting Fractions: To add or subtract fractions, they must have a common denominator. Finding equivalent fractions allows you to convert them to a common denominator.
  • Comparing Fractions: It's easier to compare fractions when they have the same denominator.

How to Use This Calculator

  1. Enter the Original Numerator (the top number of your starting fraction).
  2. Enter the Original Denominator (the bottom number of your starting fraction).
  3. Then, choose what you want to find:
    • If you know the New Numerator you want, enter it in that field.
    • If you know the New Denominator you want, enter it in that field.

    Important: You should only fill in ONE of the "New Numerator" or "New Denominator" fields. If both are filled, the calculator will prioritize finding the new numerator based on the new denominator.

  4. Click the "Calculate Equivalent Fraction" button.
  5. The calculator will display the equivalent fraction in the result area.

Examples:

Example 1: Finding a new numerator

  • Original Numerator: 3
  • Original Denominator: 4
  • New Denominator: 12
  • Result: 3/4 is equivalent to 9/12

Example 2: Finding a new denominator

  • Original Numerator: 5
  • Original Denominator: 10
  • New Numerator: 1
  • Result: 5/10 is equivalent to 1/2
function calculateEquivalentFraction() { var originalNumerator = parseFloat(document.getElementById('originalNumerator').value); var originalDenominator = parseFloat(document.getElementById('originalDenominator').value); var newNumeratorInput = document.getElementById('newNumeratorInput').value; var newDenominatorInput = document.getElementById('newDenominatorInput').value; var resultDiv = document.getElementById('result'); // Clear previous result and reset color resultDiv.style.color = '#28a745'; // Default success color resultDiv.innerHTML = "; // — Input Validation — if (isNaN(originalNumerator) || isNaN(originalDenominator)) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Please enter valid numbers for the original fraction.'; return; } if (originalDenominator === 0) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'The original denominator cannot be zero.'; return; } var newNumeratorProvided = newNumeratorInput !== "; var newDenominatorProvided = newDenominatorInput !== "; if (!newNumeratorProvided && !newDenominatorProvided) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Please provide either a New Numerator or a New Denominator.'; return; } var calculatedNumerator; var calculatedDenominator; var targetNumerator; var targetDenominator; if (newDenominatorProvided) { targetDenominator = parseFloat(newDenominatorInput); if (isNaN(targetDenominator) || targetDenominator === 0) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Invalid New Denominator. It must be a non-zero number.'; return; } calculatedNumerator = (originalNumerator / originalDenominator) * targetDenominator; resultDiv.innerHTML = originalNumerator + '/' + originalDenominator + ' is equivalent to ' + calculatedNumerator + '/' + targetDenominator; } else if (newNumeratorProvided) { targetNumerator = parseFloat(newNumeratorInput); if (isNaN(targetNumerator)) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Invalid New Numerator. It must be a number.'; return; } if (originalNumerator === 0) { if (targetNumerator === 0) { resultDiv.innerHTML = originalNumerator + '/' + originalDenominator + ' is equivalent to ' + targetNumerator + '/' + originalDenominator + ' (or any non-zero denominator).'; } else { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Cannot find an equivalent fraction if original numerator is zero and target numerator is not zero.'; } return; } calculatedDenominator = (originalDenominator / originalNumerator) * targetNumerator; if (calculatedDenominator === 0) { resultDiv.style.color = '#dc3545'; resultDiv.innerHTML = 'Calculated denominator cannot be zero. Check your inputs.'; return; } resultDiv.innerHTML = originalNumerator + '/' + originalDenominator + ' is equivalent to ' + targetNumerator + '/' + calculatedDenominator; } }

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