Quick answer
Cross-multiply to compare fractions: n₁/d₁ versus n₂/d₂ means n₁d₂ versus n₂d₁. For 3/4 and 2/3: 3 × 3 = 9 against 2 × 4 = 8, so 3/4 > 2/3.
Enter two fractions. The calculator says which is larger or whether they are equal.
Related tools: Equivalent Fractions Calculator: Fractions equal to a given fraction. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers.
How to use the Compare Fractions Calculator
- Enter numerator 1 (a whole number).
- Enter denominator 1 (a whole number, 1 or more).
- Enter numerator 2 (a whole number).
- Enter denominator 2 (a whole number, 1 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator 1 | A whole number | — |
| Denominator 1 | A whole number | ≥ 1 |
| Numerator 2 | A whole number | — |
| Denominator 2 | A whole number | ≥ 1 |
Formula and method
Formula
compare n₁d₂ with n₂d₁
IEEE-754 double precision; shown to at most 6 decimal places.
Cross-multiplication avoids rounding.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator 1 = 3; Denominator 1 = 4; Numerator 2 = 2; Denominator 2 = 3.
| Result | Value |
|---|---|
| Comparison | 3/4 > 2/3 |
Example 2
Inputs: Numerator 1 = 1; Denominator 1 = 2; Numerator 2 = 2; Denominator 2 = 4.
| Result | Value |
|---|---|
| Comparison | 1/2 = 2/4 |
Example 3
Inputs: Numerator 1 = 1; Denominator 1 = 3; Numerator 2 = 1; Denominator 2 = 2.
| Result | Value |
|---|---|
| Comparison | 1/3 < 1/2 |
The first line is the headline result (comparison). IEEE-754 double precision; shown to at most 6 decimal places.
Why cross-multiplying works
It converts both to the common denominator d₁d₂ without writing it. 3/4 = 9/12 and 2/3 = 8/12, so 9 beats 8.
Checks
Convert to decimals as a check: 0.75 and 0.667. Denominators must be at least 1. Equal fractions such as 1/2 and 2/4 give equal cross products.
Cross multiplication
To compare 3/4 and 2/3, multiply across: 3 × 3 = 9 and 2 × 4 = 8. Since 9 is larger, 3/4 is greater. Equal products mean equal fractions, such as 1/2 and 2/4.
For 5/8 and 3/5 the products are 25 and 24, so 5/8 (0.625) is greater than 3/5 (0.6).
How the result changes with numerator 1
Holding every other input at the first worked example, this table changes only numerator 1. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator 1 | Comparison |
|---|---|
| 2 | 2/4 < 2/3 |
| 3 | 3/4 > 2/3 |
| 6 | 6/4 > 2/3 |
| 12 | 12/4 > 2/3 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator 1: entering "0" shows "Denominator 1 must be at least 1." beside that field and no result.
Choosing between the Compare Fractions Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Equivalent Fractions Calculator](/math/equivalent-fractions-calculator/) | numerator and denominator | Fraction |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
| [Long Division Calculator](/math/long-division-calculator/) | dividend and divisor | Quotient |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Denominators ≥ 1
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator 1 to confirm this.
Frequently asked questions
Which is bigger, 5/8 or 3/5?
5/8, because 25 is more than 24.
What about negative fractions?
Compare as signed values.
Does it simplify?
Use the Fraction Simplifier.
Which is larger, 5/8 or 3/5?
Cross products are 5 × 5 = 25 and 3 × 8 = 24, so 5/8 is larger.
How can I compare without cross multiplying?
Rewrite both fractions over a common denominator, or convert them to decimals.
What does the Compare Fractions Calculator calculate?
Which of two fractions is larger? It returns Comparison.
What formula does the Compare Fractions Calculator use?
compare n₁d₂ with n₂d₁. Cross-multiplication avoids rounding.
What do I need to enter in the compare Fractions Calculator?
You enter Numerator 1, Denominator 1, Numerator 2 and Denominator 2.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Denominators ≥ 1.
What is an example of a compare Fractions result?
With numerator 1 3, denominator 1 4, numerator 2 2 and denominator 2 3, the comparison is 3/4 > 2/3.
Related calculators
- Equivalent Fractions Calculator — Fractions equal to a given fraction.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Percent Off Calculator — Find the sale price and savings after a percentage discount.
- Remainder Calculator — Quotient and remainder of a whole-number division.
- Reciprocal Calculator — The multiplicative inverse of a number.
- Least to Greatest Calculator — Sort numbers in ascending or descending order.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.