Comparing Fractions Calculator

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Comparing Fractions Calculator

Fraction 1

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Fraction 2

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Result

How to Compare Two Fractions

Comparing fractions determines which fraction is larger, smaller, or if they are equal in value. While some fractions are easy to visualize (like 1/2 vs 1/4), others require mathematical methods to confirm the relationship.

Methods for Comparing Fractions

  1. Cross-Multiplication Method: This is the fastest way. Multiply the numerator of the first fraction by the denominator of the second ($a \times d$) and the numerator of the second by the denominator of the first ($c \times b$). Compare the two products.
  2. Decimal Conversion: Divide the numerator by the denominator for both fractions. For example, $3/4 = 0.75$ and $5/6 \approx 0.833$. Since $0.833 > 0.75$, $5/6$ is larger.
  3. Common Denominator: Convert both fractions so they have the same denominator (usually the Least Common Multiple). Once the denominators are identical, simply compare the numerators.

Example Calculation

Compare 3/5 and 4/7:

  • Step 1 (Cross Multiply): $3 \times 7 = 21$ and $4 \times 5 = 20$.
  • Step 2 (Compare): Since 21 is greater than 20, 3/5 is greater than 4/7.
  • Step 3 (Result): $3/5 > 4/7$.
function compareFractions() { var n1 = parseFloat(document.getElementById('num1').value); var d1 = parseFloat(document.getElementById('den1').value); var n2 = parseFloat(document.getElementById('num2').value); var d2 = parseFloat(document.getElementById('den2').value); var resultBox = document.getElementById('result-box'); var comparisonDisplay = document.getElementById('comparison-display'); var explanation = document.getElementById('math-explanation'); if (isNaN(n1) || isNaN(d1) || isNaN(n2) || isNaN(d2)) { alert("Please enter valid numbers in all fields."); return; } if (d1 === 0 || d2 === 0) { alert("Denominator cannot be zero."); return; } var cross1 = n1 * d2; var cross2 = n2 * d1; var symbol = ""; var relationText = ""; if (cross1 > cross2) { symbol = ">"; relationText = "The first fraction is greater than the second fraction."; } else if (cross1 < cross2) { symbol = "<"; relationText = "The first fraction is less than the second fraction."; } else { symbol = "="; relationText = "Both fractions are equal."; } var dec1 = (n1 / d1).toFixed(4); var dec2 = (n2 / d2).toFixed(4); comparisonDisplay.innerHTML = n1 + "/" + d1 + " " + symbol + " " + n2 + "/" + d2; var htmlContent = "Step-by-Step Analysis:"; htmlContent += "1. Cross-Multiplication: " + n1 + " × " + d2 + " = " + cross1 + " and " + n2 + " × " + d1 + " = " + cross2 + "."; htmlContent += "2. Since " + cross1 + " " + symbol + " " + cross2 + ", the comparison holds true."; htmlContent += "3. Decimal Equivalent: " + n1 + "/" + d1 + " ≈ " + dec1 + " and " + n2 + "/" + d2 + " ≈ " + dec2 + "."; htmlContent += "Conclusion: " + relationText; explanation.innerHTML = htmlContent; resultBox.style.display = 'block'; }

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