# How do I solve a ratio?

Solves A : B = C : D for any missing number, and shows the ratio in simplest form, as a decimal, and as a scale factor.

- Page: https://www.acalculator.org/math/ratio-calculator
- JSON spec: https://www.acalculator.org/math/ratio-calculator.json
- Version: 408755f4ced8

## Default answer

Example with the default inputs (A 3, B 4, C 6): 3 : 4 = 6 : 8.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| a | A | The first term of the first ratio, A : B. |
| b | B | The second term of the first ratio, A : B. |
| c | C | The first term of the second ratio, C : D. |
| d | D | The second term of the second ratio, C : D. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| A | A | The first term of the first ratio, A : B. |
| B | B | The second term of the first ratio, A : B. |
| C | C | The first term of the second ratio, C : D. |
| D | D | The second term of the second ratio, C : D. |
| simplest | Simplest form | A : B in lowest whole-number terms, such as 3 : 4. |
| decimal | As a decimal | The value of the ratio: A ÷ B. |
| scale | Scale factor | How many times bigger C : D is than A : B: C ÷ A. |

## Method

A : B = C : D means A ÷ B = C ÷ D, so A × D = B × C.

## Assumptions

- All four terms are more than 0.
- The simplest form is shown when it needs whole numbers of a billion or less; decimals are taken exactly as they print (0.1 is 1/10).

## Worked examples

1. a = 3, b = 4, c = 6 gives d = 8, simplest = 3 : 4, decimal = 0.75, scale = 2. Source: hand calculation in content.mdx: D = 4 × 6 ÷ 3 = 8.
2. a = 5, c = 15, d = 21 gives b = 7, scale = 3. Source: hand calculation in content.mdx: B = 5 × 21 ÷ 15 = 7.
3. a = 1.5, b = 2, c = 4.5 gives d = 6, simplest = 3 : 4, decimal = 0.75. Source: hand calculation in content.mdx: D = 2 × 4.5 ÷ 1.5 = 6; 1.5 : 2 = 15 : 20 = 3 : 4.
4. b = 9, c = 32, d = 18 gives a = 16, simplest = 16 : 9. Source: hand calculation in content.mdx: A = 9 × 32 ÷ 18 = 16.
5. a = 1,920, b = 1,080, d = 720 gives c = 1,280, simplest = 16 : 9. Source: hand calculation in content.mdx: C = 1920 × 720 ÷ 1080 = 1280; 1920 : 1080 = 16 : 9.

## FAQ

### How do I solve a ratio with a missing number?

Write the two ratios as equal fractions and cross-multiply. For 3 : 4 = 6 : D, write 3 ÷ 4 = 6 ÷ D, so 3 × D = 4 × 6 = 24 and D = 8.

### How do I simplify a ratio?

Divide both numbers by their greatest common factor. 1920 : 1080 has a greatest common factor of 120, so it simplifies to 16 : 9. For decimals, first multiply both numbers by the same power of 10 to make them whole: 1.5 : 2 becomes 15 : 20, which is 3 : 4.

### What is the difference between a ratio and a proportion?

A ratio compares two amounts, such as 3 : 4. A proportion says that two ratios are equal, such as 3 : 4 = 6 : 8. This calculator solves proportions: it finds the number that makes the two ratios equal.

### How do I scale a ratio up or down?

Multiply or divide both numbers by the same scale factor. 3 : 4 scaled by 2 is 6 : 8, and scaled by 0.5 is 1.5 : 2. The calculator shows the scale factor C ÷ A between the two ratios.

### How are ratios used for screen sizes?

A screen's aspect ratio compares its width with its height. Full HD, 1920 × 1080 pixels, is 16 : 9. To find the width of a 16 : 9 picture that is 720 pixels tall, solve 1920 : 1080 = C : 720, which gives C = 1280.

### Can a ratio be turned into a fraction or a percentage?

Yes, as a part of the whole. In a ratio of 3 : 4, the first part is 3 out of 3 + 4 = 7 parts, so it is 3/7 of the total, about 42.86%. The ratio's own value, 3 ÷ 4 = 0.75, compares the first part with the second part, not with the total.

## Sources

- OpenStax, Elementary Algebra 2e, section 8.7 Solve Proportion and Similar Figure Applications: https://openstax.org/books/elementary-algebra-2e/pages/8-7-solve-proportion-and-similar-figure-applications