Compare and order fractions
Compare two or more fractions, decimals and mixed numbers. Order them exactly and see the common-denominator explanation.
Fraction calculator with exact steps
Calculate with whole numbers, finite decimals, fractions or mixed numbers. Exact fraction arithmetic keeps the numerator and denominator as integers, so 0.1 + 0.2 becomes 3/10 without a binary floating-point artifact.
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 + 5/16 = 11/16.
- The least common denominator is 16.
- Rewrite 3/8 as 6/16, then add the numerators.
- The numerator 11 and denominator 16 have greatest common divisor 1.
Add 3/8 and 5/16
Imagine two lengths measured in the same unit. Express both using sixteenths before adding them.
3/8 = 6/16
6/16 + 5/16 = 11/16
11/16 = 0.6875The sum is larger than either positive addend. That quick reasonableness check can catch using 8 + 16 as the denominator by mistake.
Four operations, one exact representation
Addition and subtraction require equivalent fractions with a common denominator. Multiplication combines numerators and denominators directly. Division multiplies the first fraction by the reciprocal of the second; a zero divisor has no reciprocal.
A greatest-common-divisor reduction removes factors shared by the numerator and denominator. The denominator is kept positive, and a zero result is represented as 0/1. A mixed number such as -1 1/2 means negative one and one half, or -3/2.
a/b + c/d = (ad + bc)/(bd)
a/b − c/d = (ad − bc)/(bd)
a/b × c/d = ac/(bd)
a/b ÷ c/d = ad/(bc), c ≠ 0Input limits and common mistakes
Use a slash for a fraction: 3/8. For a mixed number, separate the whole part with a space: 1 3/8. A negative sign applies to the entire mixed number. Do not enter expressions, units or a repeating-decimal ellipsis.
Integer components are limited to 256 digits; finite decimal exponents are bounded to ±300. Denominators and divisors must be nonzero. The fraction result is exact; any displayed decimal is only an approximation.
Questions about fraction arithmetic
Why not add the denominators?
The denominator names the size of each part. Adding different-sized parts requires renaming them with one common size first.
Can I enter 0.125?
Yes. A finite decimal is converted exactly to an integer divided by a power of ten, then simplified.
Does the tool accept repeating decimals?
No. Enter an exact fraction such as 1/3 instead of 0.333… or a rounded decimal.
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: multiplying and dividing fractions — Reciprocals, reduction and fraction operations.
- OpenStax: adding unlike fractions — Equivalent fractions and least common denominators.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
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Further reading
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