Comparing Fractions Calculator
Compare two fractions to see which is larger.
Decide which of two fractions is bigger.
How the Math Works
The Comparing Fractions Calculator uses the cross-multiplication method to determine which of two fractions is larger. Given fractions a/b and c/d, the calculator multiplies a by d and c by b, then compares these products. If a·d is greater than c·b, then a/b is the larger fraction; if a·d is less than c·b, then c/d is larger. This works because cross-multiplying eliminates the denominators, allowing direct comparison of the numerators' relative sizes. The cross-products represent equivalent numerators when both fractions are expressed with a common denominator.
Practical Applications
To use this calculator for comparing fractions like 3/4 and 5/7, simply enter the numerators and denominators into their respective fields. The calculator quickly performs the cross-multiplication: 3·7=21 and 5·4=20. Since 21>20, the calculator determines that 3/4 is larger than 5/7. This method is particularly useful when working with fractions that have different denominators, as it bypasses the need to find a common denominator manually. You can use this tool for homework problems, recipe scaling, or any situation requiring fraction comparison.
Day-to-Day Use
In everyday life, this calculator helps with practical decisions involving proportions and comparisons. When shopping, you can quickly determine which size product offers better value by comparing unit prices expressed as fractions. In cooking, you can easily check if you have enough ingredients by comparing recipe proportions. When splitting bills or dividing resources among friends, the calculator helps ensure fair distribution by comparing fractional shares. Students benefit from faster homework completion and better understanding of fraction relationships, while anyone making proportional decisions—from comparing interest rates to adjusting medication dosages—can rely on this tool for quick, accurate comparisons.
Worked example
3/5 vs 2/3 → 9 vs 10 → second is larger.
FAQ
Equal?
When the cross-products match.