Comparing Fractions
Compare two fractions using cross-multiplication. Shows which is larger, smaller, or equal. Free online tool with decimal conversion for students and teachers.
About This Calculator
The Comparing Fractions Calculator lets you compare any two fractions a/b and c/d in an instant. Enter the numerator and denominator for each fraction, then click Calculate to see which fraction is larger, which is smaller, or whether they are exactly equal. The tool uses the standard cross-multiplication method taught in schools worldwide: multiply a x d and b x c, then compare the two products.
This calculator is ideal for students learning fraction comparison, teachers preparing lesson examples, parents helping with homework, and anyone who needs to quickly compare fractional values. The decimal equivalent of each fraction is also displayed, giving you both a symbolic and numerical understanding of the relationship.
The cross-multiplication approach works for any pair of positive or negative fractions, regardless of whether the denominators are the same or different. Simply enter your four values, click Calculate, and the result shows the correct inequality sign (>, <, or =) between the two fractions.
Frequently Asked Questions
How does comparing fractions work?
Comparing fractions uses cross-multiplication: multiply the numerator of the first fraction by the denominator of the second (a x d) and the numerator of the second by the denominator of the first (b x c). If axd > bxc, then a/b > c/d. If axd < bxc, then a/b < c/d. If they are equal, the fractions are equivalent. The calculator also shows each fraction as a decimal for easy visual comparison.
What does the comparison result tell me?
The calculator displays which fraction is greater (a/b > c/d), which is smaller (a/b < c/d), or if they are equal (a/b = c/d). It also shows the decimal value of each fraction rounded to six decimal places, so you can see the difference numerically.
Can I compare fractions with different denominators?
Yes, the calculator handles fractions with any denominators, same or different. Cross-multiplication works universally for any pair of positive fractions regardless of whether the denominators match.
Can I compare negative fractions?
Yes, you can enter negative numerators or denominators. The calculator will cross-multiply and compare them correctly, showing the proper inequality sign in the result.
What if I enter zero as the denominator?
A zero denominator is undefined in mathematics. The calculator will not compute a result if any denominator is zero. Please enter non-zero values for both denominators (b and d).
Is this fraction comparison tool free to use?
Yes, all calculators on Calculy including the Comparing Fractions Calculator are completely free to use with no limits, registration, or hidden charges.
How accurate are the decimal results shown?
Decimal values are shown to six decimal places, which is sufficient for virtually all comparison needs. The cross-multiplication comparison itself is perfectly accurate since it uses exact integer arithmetic.
What are equivalent fractions and how does this tool handle them?
Equivalent fractions are different fractions that represent the same value (e.g., 1/2 = 2/4 = 3/6). When the cross-multiplication result axd equals bxc, the tool will display that the two fractions are equal, meaning they are equivalent.