Fraction arithmetic
Add, subtract, multiply or divide fractions and mixed numbers. See exact simplified results, common denominators and each calculation step.
Compare fractions: order values with exact steps
Find which fraction is larger without relying on rounded decimals. Compare two values or sort a list of up to 20 fractions, mixed numbers and finite decimals. Equal values remain equal after simplification.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
3/8 is greater than 5/16.
- The common denominator is 16.
- The first fraction equals 6/16; the second equals 5/16.
- Since 6 > 5, the first fraction is larger.
Which is larger: 3/8 or 5/16?
The denominators 8 and 16 describe different-sized pieces. Convert the eighths into sixteenths to compare the number of equal-sized pieces.
3/8 = 6/16
5/16 = 5/16
6/16 > 5/16
Difference = 1/16A larger denominator does not automatically mean a larger fraction. With the same positive numerator, it means smaller pieces. With different numerators, compare equivalent fractions or cross products.
Compare values, not digit sizes
For two fractions with positive denominators, cross multiplication compares ad and cb without rounding either value. Negative denominators are normalized before comparison.
For a longer list, the tool sorts using exact cross products. A shared least common denominator is shown as a second explanation. Equivalent inputs such as 1/2, 2/4 and 0.5 occupy the same position in value even if their original spelling differs.
a/b ? c/d
With b > 0 and d > 0, compare a × d with c × b.
LCM denominator L: a/b = (a × L/b)/LInput limits and common mistakes
Enter 2–20 values separated by commas, semicolons or new lines. Do not use commas inside a number. Mixed numbers can contain an internal space, so spaces alone are not list separators.
The integer and exponent limits match the fraction calculator. Fractions with a zero denominator are rejected. Output is a mathematical ordering, not a conversion between different physical units.
Questions about compare and order fractions
Is 3/8 bigger than 5/16?
Yes. They are 6/16 and 5/16, respectively. Their exact difference is 1/16.
How are negative fractions ordered?
A value farther below zero is smaller. For example, -3/4 < -1/2 even though 3/4 > 1/2.
Can a decimal and a fraction be equal?
Yes. The finite decimal 0.5 is exactly 1/2, so it compares equal to 2/4.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- OpenStax: equivalent fractions and denominators — Using equivalent fractions with a common denominator.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
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Further reading
All calculators and developer tools · Source-checked guides · How Ithy checks sources