# How do I solve a proportion?

Solves the proportion a/b = c/d for the missing number by cross-multiplication, as an exact fraction and a decimal, or checks whether four numbers form a proportion.

- Page: https://www.acalculator.org/math/proportion-calculator
- JSON spec: https://www.acalculator.org/math/proportion-calculator.json
- Version: 0706eb4d40ad

## Default answer

Example with the default inputs (a 3, b 4, d 10): The missing number in the proportion is 7.5 (15/2).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| a | a | The top of the first fraction, a/b. |
| b | b | The bottom of the first fraction, a/b. It cannot be 0. |
| c | c | The top of the second fraction, c/d. Leave the number to find empty. |
| d | d | The bottom of the second fraction, c/d. It cannot be 0. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| x | Missing number | The number that makes a/b = c/d true, in place of the box left empty. |
| fraction | Missing number as a fraction | The missing number as an exact fraction in lowest terms. |
| proportional | Do the four numbers form a proportion? | With all four numbers typed: Yes when a × d = b × c exactly, else No. |
| ratio | Value of a/b | The first fraction a/b in lowest terms. |
| steps | Cross-multiplication | The working: cross-multiply, then divide by the number next to the unknown. |

## Method

a/b = c/d means a × d = b × c (cross-multiplication); divide by the number next to the unknown.

## Assumptions

- b and d are the bottoms of the fractions and cannot be 0.
- Every number is read exactly as typed (0.1 is 1/10), and the arithmetic is exact before rounding for display.
- With all four numbers typed, the calculator checks whether they form a proportion instead.

## Worked examples

1. a = 3, b = 4, d = 10 gives x = 7.5, fraction = 15/2, ratio = 3/4, steps = Cross-multiply: 3 × 10 = 4 × c; 4 × c = 30; c = 30 ÷ 4 = 15/2; As a decimal: c = 7.5. Source: OpenStax, Prealgebra 2e, §6.5, cross products (https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications).
2. a = 5, c = 20, d = 36 gives x = 9, fraction = 9, ratio = 5/9.
3. b = 3, c = 2, d = 7 gives x = 0.857143, fraction = 6/7.
4. a = 0.1, b = 0.3, c = 5 gives x = 15, fraction = 15, ratio = 1/3.
5. a = -2, b = 5, d = 8 gives x = -3.2, fraction = -16/5.
6. a = 3, b = 4, c = 9, d = 12 gives proportional = yes, ratio = 3/4.
7. a = 2, b = 3, c = 5, d = 7 gives proportional = no.

## FAQ

### How do I solve a proportion?

Cross-multiply, then divide. In 3/4 = c/10, multiply across the equals sign: 4 × c = 3 × 10 = 30. Divide both sides by 4: c = 30 ÷ 4 = 7.5.

### What is a proportion?

A proportion is an equation that says two ratios (fractions) are equal, such as 3/4 = 9/12. Both sides have the same value, 0.75, so the four numbers are in proportion.

### Why does cross-multiplication work?

Multiplying both sides of a/b = c/d by b × d clears the fractions and leaves a × d = b × c. It is the same equation, so any number that makes one true makes the other true, as long as b and d are not 0.

### How do I check if two ratios form a proportion?

Type all four numbers. The calculator compares the cross products exactly: 3/4 and 9/12 give 3 × 12 = 36 and 4 × 9 = 36, so they form a proportion; 2/3 and 5/7 give 14 and 15, so they do not.

### Can the numbers be decimals, fractions, or negative?

Yes. Decimals are read exactly (0.1 is one tenth, not a rounded binary value), negatives work, and the answer is shown as an exact fraction in lowest terms and as a decimal. Only the bottoms b and d cannot be 0.

### Why does it say there is no single answer?

When the number next to the unknown in its cross product is 0, the equation does not fix the unknown. In 0/5 = 0/d, any d works; in 0/5 = 3/d, no d works, because 0/5 is 0 and 3/d never is.

### Is a proportion the same as a ratio?

A ratio compares two numbers (3 to 4). A proportion says two ratios are equal (3 : 4 = 9 : 12). For ratios written with a colon, the ratio calculator solves the same equation.

## Sources

- OpenStax, Prealgebra 2e, §6.5 Solve Proportions and their Applications (cross products: a/b = c/d means ad = bc). https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications