Quick answer
To solve a/b = c/d for the unknown, cross-multiply: a·d = b·c. With 1/2 = 3/d, d = 6.
Enter three of the four values and leave one blank. The calculator returns the unknown. Use this solve for unknown fraction (cross multiplication) to check your own figures.
Related tools: Cross Product Calculator: Cross product of two 3-D vectors. Matrix Multiplication Calculator: Multiply two matrices. Slope Calculator: Slope, angle, distance and line equation through two points.
How to use the Solve for Unknown Fraction (Cross Multiplication)
- Optionally, enter a.
- Optionally, enter b.
- Optionally, enter c.
- Optionally, enter d.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| a (optional) | A number. Leave exactly one blank | — |
| b (optional) | A number. Leave exactly one blank | — |
| c (optional) | A number. Leave exactly one blank | — |
| d (optional) | A number. Leave exactly one blank | — |
Formula and method
Formula
a/b = c/d → a·d = b·c
IEEE-754 double precision; shown to at most 6 decimal places.
Cross-multiply and solve for the blank value.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: a = 1; b = 2; c = 3.
| Result | Value |
|---|---|
| Unknown (d) | 6 |
Example 2
Inputs: b = 4; c = 6; d = 8.
| Result | Value |
|---|---|
| Unknown (a) | 3 |
Example 3
Inputs: a = 2; c = 5; d = 10.
| Result | Value |
|---|---|
| Unknown (b) | 4 |
The first line is the headline result (unknown (d)). IEEE-754 double precision; shown to at most 6 decimal places.
Cross multiplication
1/2 = 3/d gives 1 × d = 2 × 3, so d = 6. Check: 3/6 = 1/2 ✓. It is the standard method for proportions.
Uses
Scale a recipe (2 cups for 4 people, how many for 10?), convert units and solve similar-triangle problems. Exactly one value must be blank, and divisors must be non-zero.
How the result changes with a
Holding every other input at the first worked example, this table changes only a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| a | Unknown (d) |
|---|---|
| 0.5 | 12 |
| 1 | 6 |
| 2 | 3 |
| 4 | 1.5 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- a: entering "1" shows "Leave exactly one field blank." beside that field and no result.
- d: entering "0" shows "A denominator must not be 0." beside that field and no result.
Choosing between the Solve for Unknown Fraction (Cross Multiplication) 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 |
|---|---|---|
| [Cross Product Calculator](/math/cross-product-calculator/) | vector A and vector B | Cross product |
| [Matrix Multiplication Calculator](/math/matrix-multiplication-calculator/) | matrix A and matrix B | A × B |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- Exactly one blank
- Divisors must be non-zero
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 a and d to confirm this.
Frequently asked questions
What is x in 3/5 = x/20?
Cross-multiply: 3 × 20 = 5x, so x = 12.
What is a proportion?
An equation of two ratios.
Does the blank position matter?
No, any one can be unknown.
What does the Solve for Unknown Fraction (Cross Multiplication) calculate?
Solve a/b = c/d when one value is unknown. It returns Unknown (d).
What formula does the Solve for Unknown Fraction (Cross Multiplication) use?
a/b = c/d → a·d = b·c. Cross-multiply and solve for the blank value.
What do I need to enter in the solve for Unknown Fraction (Cross Multiplication)?
You enter . Optional: a, b, c and d.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Exactly one blank.
What are the limits of this calculator?
Exactly one blank. Divisors must be non-zero.
What is an example of a solve for Unknown Fraction (Cross Multiplication) result?
With a 1, b 2 and c 3, the unknown (d) is 6.
Related calculators
- Cross Product Calculator — Cross product of two 3-D vectors.
- Matrix Multiplication Calculator — Multiply two matrices.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
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.