Compare Fractions Calculator

Enter two or more fractions, mixed numbers or decimals separated by commas, and the calculator tells you which is larger and puts them in order from least to greatest, or greatest to least. It rewrites every value over the least common denominator so the comparison is easy to see, gives each as a decimal, and marks any that are equal. A number line shows where each value falls. It accepts entries typed as 3/4, mixed numbers typed as 1 1/2, decimals such as 0.6, and negative numbers.

Cross-multiplication: a/b > c/d exactly when a × d > c × b (for positive denominators)

To compare 3 over 434 and 5 over 858, multiply across: 3 × 8 = 24 and 5 × 4 = 20. Since 24 is larger, 3 over 434 is the larger fraction. This works for any pair and avoids decimals entirely.

For a list, a common denominator is clearer. The least common denominator of 4, 8 and 3 is 24, so 3 over 434 becomes 18 over 241824, 5 over 858 becomes 15 over 241524 and 2 over 323 becomes 16 over 241624. Now compare the numerators: 15 < 16 < 18, so the order from least to greatest is 5 over 858, 2 over 323, 3 over 434.

• Same denominator: the larger numerator is the larger fraction.
• Same numerator: the smaller denominator is the larger fraction, since the whole is cut into fewer, bigger pieces.
• Benchmark one half: a fraction is more than a half when its numerator is more than half its denominator, which settles many comparisons at a glance.
• Distance from one: fractions just below one can be compared by how much is missing; a piece missing from a larger denominator is smaller.

Compare mixed numbers by their whole-number parts first; only if those are equal do you need to compare the fractions. The calculator converts mixed numbers to improper fractions, so 1 1/4 becomes five quarters. Decimals are converted to exact fractions, so 0.75 equals three quarters exactly. For negative numbers the order reverses: a negative half is less than a negative third, because it is farther below zero.

Fractions that name the same amount, such as two quarters and one half, are equivalent. Cross-multiplication gives equal products for them, and over a common denominator they have the same numerator. The calculator simplifies every input and shows an equals sign between equivalent values in the ordered list. For adding, subtracting or simplifying fractions, use the fraction calculator.

1. Type the fractions separated by commas. Put a space between the whole number and the fraction in a mixed number.
2. Choose least to greatest or greatest to least.
3. Read the ordered list, then check each value over the common denominator to see why the order is what it is.

Comparing fractions comes up more often than it seems: choosing between recipe measures, comparing drill bit or wrench sizes in inches, reading odds, or working out which discount is bigger. Converting to a common denominator or to decimals, as this calculator does, makes any of these comparisons quick.

In the Common Core standards, comparing fractions with different numerators and denominators is a grade 4 skill, building on comparing fractions with the same numerator or denominator in grade 3. Students are expected to explain their reasoning, for example by drawing fraction bars or using benchmarks like one half, so it is worth trying a comparison by hand before checking it here.