Comparing fractions means deciding which one is bigger, and it is harder than it looks when the pieces are different sizes. Three reliable methods cover every case. You can check your work with the free tools on Calc Solver.
Method 1: Use a Common Denominator
Rewrite both fractions with the same denominator, then compare the numerators. To compare 3/4 and 5/6, convert both to twelfths: 3/4 becomes 9/12 and 5/6 becomes 10/12. Since 10 is bigger than 9, 5/6 is bigger than 3/4. This method always works, but it takes the most steps.
Method 2: Cross-Multiplication
Multiply the numerator of each fraction by the denominator of the other. To compare 2/3 and 3/5, compute 2 times 5 = 10 and 3 times 3 = 9. The larger product belongs to the larger fraction, so 2/3 is bigger than 3/5. Cross-multiplication is the fastest method when you only need to know which fraction wins.
Method 3: Compare to a Benchmark
Compare each fraction to a friendly value like 1/2. The fraction 5/8 is bigger than 1/2, while 3/7 is smaller than 1/2, so 5/8 must be bigger than 3/7 without any computation. Benchmarks are fastest when the fractions fall on opposite sides of 1/2, 0, or 1.
Which Method to Use When
Use benchmarks for a quick estimate, cross-multiplication for a fast exact answer, and common denominators when you also need to add, subtract, or order several fractions. All three methods agree when used correctly, so pick the one that fits the problem.
Common Mistakes to Avoid
First, assuming the fraction with the bigger numbers is bigger, which fails often: 1/8 is smaller than 1/4 even though 8 is bigger than 4. Second, cross-multiplying in the wrong direction and flipping the answer. Third, comparing fractions with different wholes, which makes the comparison meaningless.
Practice Problems to Try
Compare 4/5 and 7/9, then 3/8 and 2/5, then order 1/2, 3/5, and 5/8 from smallest to largest. Try each problem with two different methods and confirm both give the same result.