Comparing Fractions Calculator
Compare two fractions or mixed numbers by converting both to a common denominator, with a step-by-step derivation and the greater-than/less-than/equal verdict.
Input
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/comparing-fractions-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"wholeA": "",
"numeratorA": "3",
"denominatorA": "4",
"wholeB": "",
"numeratorB": "2",
"denominatorB": "3"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `comparing-fractions-calculator` tool (Comparing Fractions Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/comparing-fractions-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Comparing Fractions Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
What does this calculator do?
Enter two fractions — or mixed numbers, like 1 3/4 — and this tool tells you which one is bigger, smaller, or whether they're equal. It does this the way you'd do it by hand: by converting both fractions to a common denominator first, then comparing the numerators.
How to use it
- For Fraction A, enter an optional whole number and a numerator/denominator. Leave the whole number blank for a simple fraction, or fill it in for a mixed number (e.g. whole
1, numerator3, denominator4for1 3/4). - Do the same for Fraction B.
- Read the verdict, the simplified/decimal form of each fraction, and the step-by-step common-denominator conversion.
The math
Two fractions can't be compared directly unless they share a denominator. This calculator finds the least common multiple (LCM) of the two denominators, scales each fraction up to that common denominator, and compares the resulting numerators:
a/b vs. c/d
LCM(b, d) = L
a/b = (a × L/b) / L
c/d = (c × L/d) / L
Compare (a × L/b) vs (c × L/d)Whichever scaled numerator is larger belongs to the larger fraction — since both now sit over the same denominator, comparing numerators is exactly equivalent to comparing the original fractions.
Comparing vs. checking equivalence
This is a different question from "are these two fractions equal?" — for that, see the Equivalent Fractions Calculator's Check Equivalence mode, which uses cross-multiplication and only answers yes/no. This tool always shows the full ordering (greater than, less than, or equal to) and the common-denominator work, not just an equivalence check.
Example use cases
- Homework and teaching — see exactly how a common-denominator comparison is done, step by step, rather than just getting an answer.
- Recipe scaling — quickly tell whether
3/4cup or2/3cup is more before halving or doubling a recipe. - Measurements — compare fractional measurements (in inches, for example) without converting to decimals first.
Privacy
All calculations run locally in your browser — your input is never sent to a server.
Related tools
To check whether two fractions are equivalent instead of ordering them, use the Equivalent Fractions Calculator. For general fraction-decimal conversion and arithmetic, see Fraction ⇄ Decimal.