Proportion Calculator
Solve a proportion of the form a/b = c/x for the unknown x by cross-multiplying, with every step shown.
Calculator
- Cross-multiplication
- Solves for the unknown
- Exact fraction form
- Equality proof
Result & calculation receipt
- Method
- Cross-multiplication of the proportion a/b = c/x
- Formula
a/b = c/x ⟹ a·x = b·c ⟹ x = b·c / a- Substitution
- 6 = (3 × 4) ÷ 2
- Steps
- Cross-multiply: 2·x = 3·4 = 12.
- Divide by 2: x = 12 ÷ 2 = 6.
- Verification
- 2/3 = 0.666667 and 4/6 = 0.666667 — the two ratios match.
- Exact result
- 6
- Decimal result
- 6
- Engine
- math-solvers v1.4.0
How this calculator works
A proportion states that two ratios are equal. The calculator cross-multiplies — a times x equals b times c — and then divides by a to isolate x. It reports x as an exact fraction when it is not a whole number and as a decimal, and checks the answer by confirming that the two ratios evaluate to the same value.
Worked example
For 2/3 = 4/x, cross-multiplying gives 2x = 3 × 4 = 12, so x = 12 ÷ 2 = 6. The check confirms 2/3 = 0.667 and 4/6 = 0.667 — the ratios match. This is the same reasoning behind scaling a recipe, converting units, or reading a map.
Key insight
Cross-multiplication works because multiplying both sides of a/b = c/x by b·x clears the denominators. Proportions are the workhorse of everyday scaling problems: "if 2 costs 3, what do 4 cost?" is just a proportion in disguise.
Frequently asked questions
What is a proportion?
A proportion is a statement that two ratios are equal, such as 2/3 = 4/x. Solving it means finding the value that makes both ratios the same.
How does cross-multiplication solve it?
In a/b = c/x, the cross-products are equal: a × x = b × c. Dividing both sides by a gives x = b × c ÷ a. The calculator shows the cross-product and the division.
What if a is zero?
Solving for x requires dividing by a, so a cannot be zero. The calculator returns a structured error in that case.
Can the answer be a fraction?
Yes. When x is not a whole number the calculator gives the exact fraction as well as the decimal, so nothing is lost to rounding.
How is the answer checked?
It substitutes x back and confirms the two ratios a/b and c/x evaluate to the same number, which is shown in the receipt.
Methodology & verification
The proportion a/b = c/x is solved by cross-multiplication: a·x = b·c, so x = b·c ÷ a. The value a must be non-zero; other invalid inputs return structured errors. The result is given as an exact fraction (when non-integer) and as a decimal. Verification substitutes x back and confirms the ratios a/b and c/x are equal.
Engine: math-solvers v1.4.0 · Last reviewed: · Every result is computed client-side and never sent to a server. See the verification methodology and the scientific calculator validation.