Find the missing number in a proportion (A:B = C:D), or simplify a ratio to lowest terms, decimals included. Pick a mode, fill in what you know and leave the unknown blank.
Enter a ratio like 10 : 15 and it reduces to lowest terms by dividing both sides by their greatest common divisor. Decimals are supported.
Enter three of the four values in A : B = C : D and leave the unknown blank. The calculator solves for the missing one (cross-multiplication).
A ratio compares two quantities. Simplifying keeps the same proportion with the smallest whole numbers; solving a proportion finds an unknown that keeps two ratios equal.
How to Find the Missing Number in a Proportion
Cross-multiply the two known numbers that sit diagonally opposite each other, then divide by the number diagonal to the blank. In 4 : 6 = ? : 15, multiply 4 × 15 = 60 and divide by 6, so the missing number is 10. Check it: 4 ÷ 6 and 10 ÷ 15 both come to 0.667.
| Proportion | Working | Missing number |
|---|---|---|
| 4 : 6 = ? : 15 | 4 × 15 ÷ 6 | 10 |
| 3 : 5 = 12 : ? | 5 × 12 ÷ 3 | 20 |
| 3 : ? = 9 : 12 | 3 × 12 ÷ 9 | 4 |
| ? : 8 = 5 : 20 | 8 × 5 ÷ 20 | 2 |
| 1.5 : 2 = 6 : ? | 2 × 6 ÷ 1.5 | 8 |
To solve a proportion using cross multiplication by hand, take 3 : 5 = 12 : ?:
- Write it as fractions: 3/5 = 12/D.
- Cross-multiply: 3 × D = 5 × 12 = 60.
- Divide: D = 60 ÷ 3 = 20.
- Check: 3 ÷ 5 = 0.6 and 12 ÷ 20 = 0.6.
How the Two Modes Work
“Simplify ratio” reduces one ratio to lowest terms, and “Solve proportion” finds one blank term when two ratios are equal.
Formula: To simplify A : B, any decimal terms are first scaled up by a power of 10 until both become whole numbers, then both are divided by their greatest common factor (GCF) to get the reduced ratio. To solve a proportion A : B = C : D where exactly one term is left blank, the calculator cross-multiplies to isolate it: if A is missing, A = (B × C) ÷ D; if B is missing, B = (A × D) ÷ C; if C is missing, C = (A × D) ÷ B; if D is missing, D = (B × C) ÷ A.
A and B are the first ratio; C and D are used only in Solve Proportion mode. Leave whichever term is unknown blank.
Example Scenarios
| A | B | C | D | Result |
|---|---|---|---|---|
| 10 | 15 | – | – | Simplifies to 2 : 3 |
| 8 | 20 | – | – | Simplifies to 2 : 5 |
| 2.5 | 5 | – | – | Simplifies to 1 : 2 |
| 4 | 6 | ? | 15 | C = 10 |
| 3 | ? | 9 | 12 | B = 4 |
| ? | 8 | 5 | 20 | A = 2 |
How to Simplify Ratios With Decimals
Scale both terms up by 10 or 100 until they are whole, then divide by the greatest common factor. 2.5 : 5 becomes 25 : 50, and dividing by 25 gives 1 : 2. 1.2 : 0.8 becomes 12 : 8, and dividing by 4 gives 3 : 2.
Practical Uses: Screens, Recipes and Mixes
Keep the terms in the same order and the same units. 250 g to 1 kg is 1:4, not 250:1, and flour to water at 3:2 is not 2:3. To scale a recipe, set it up as A:B = C:D with the new amount as C and solve for D.
What is the 1920×1080 aspect ratio? Both numbers divide by 120, giving 16:9, which helps you resize without distortion. To work out the ratio of 3 numbers, such as 12:18:30, divide all three by their common factor of 6 to get 2:3:5. The ratio article on Wikipedia covers the notation and terms in more depth.
Common questions about ratios and proportions
How do you solve a proportion using cross multiplication?
Write A:B = C:D as A/B = C/D, so A × D = B × C. Multiply the two known terms that sit diagonally opposite each other, then divide by the term diagonal to the blank. In 3:5 = 12:?, 5 × 12 = 60 and 60 ÷ 3 = 20.How do you simplify ratios with decimals?
Multiply both terms by 10, 100 or more until they are whole, then divide by their greatest common factor. 2.5:5 becomes 25:50, and dividing by 25 gives 1:2.What is the 1920×1080 aspect ratio?
1920 and 1080 share a greatest common factor of 120, so 1920:1080 reduces to 16:9, the standard widescreen shape.How do you work out the ratio of 3 numbers?
Find the greatest common factor of all three and divide each by it. For 12:18:30 the common factor is 6, so the ratio is 2:3:5. This tool takes two terms, so do three-part ratios by hand or one pair at a time.What’s the difference between simplifying a ratio and solving a proportion?
Simplifying takes one ratio, like 10:15, and reduces it to the smallest whole numbers with the same relationship (2:3). Solving a proportion takes two ratios set equal, like 4:6 = ?:15, and finds the missing term (10).What happens if I enter zero as one of the terms?
A zero in the B or D position makes the ratio undefined, since you can’t divide by zero. The calculator shows an error instead of a result, so check your inputs if you see one.Related Calculators
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