Proportion Formula and How to Solve for X
A proportion says two ratios are equal: A / B = C / D. Cross-multiply to get A × D = B × C, then divide by the number paired with x. If 3 / 12 = x / 30, then 12x = 90 and x = 7.5. Two ratios are proportional only when both cross products match.
Every proportion problem reduces to one equation. Write the known ratio and the ratio with the unknown as two fractions, set them equal, and cross-multiply so the fractions disappear.
Formula for x in each position
| Unknown | Formula |
|---|---|
| A (first numerator) | A = (B × C) ÷ D |
| B (first denominator) | B = (A × D) ÷ C |
| C (second numerator) | C = (A × D) ÷ B |
| D (second denominator) | D = (B × C) ÷ A |
Proportion Examples: Solving for X Step by Step
Most real-world proportion problems follow the same pattern: keep the units in the same place in both fractions, cross-multiply, then divide. Enter the three known numbers above to get the same steps for your own values.
Scaling a Recipe
A recipe uses 3 cups of flour for 12 cookies. How much flour do you need for 30 cookies?
You need 7.5 cups of flour.
Reading a Map Scale
On a map, 1 cm represents 25 km. Two towns are 6.4 cm apart on the map. How far apart are they?
The towns are 160 km apart.
Comparing Unit Prices
5 kg of apples cost $8. At the same price per kilogram, what do 8 kg cost?
8 kg cost $12.80.
Medication Dosage
A dose is 15 mg per 10 kg of body weight. What is the dose for a 32 kg child?
The dose is 48 mg. Always confirm dosages with a pharmacist or doctor.
Direct vs Inverse Proportion
Direct proportion
Both quantities change in the same direction: twice the cookies need twice the flour. The ratio y ÷ x stays constant, so x₁ / y₁ = x₂ / y₂.
Inverse proportion
One quantity goes up as the other goes down: twice the workers finish in half the time. The product x × y stays constant, so x₁ × y₁ = x₂ × y₂.
Example: 4 workers paint a house in 6 days. 3 workers need (4 × 6) ÷ 3 = 8 days. A car at 60 km/h takes 5 hours; at 75 km/h it takes (60 × 5) ÷ 75 = 4 hours.
How to Check if Two Ratios Are Proportional
Multiply the outer terms (A × D) and the inner terms (B × C). If the products are equal, the ratios form a proportion. 4 : 6 and 10 : 15 are proportional because 4 × 15 = 60 and 6 × 10 = 60. 2 : 3 and 5 : 7 are not, because 14 ≠ 15. You can also divide: 4 ÷ 6 and 10 ÷ 15 both equal 0.667.
Need to simplify a ratio or split an amount?
Use the ratio calculator to reduce ratios to lowest terms, resize 16:9 dimensions or divide a total by 2 : 3 : 5.
Preguntas frecuentes
How do you solve a proportion for x?
Write the proportion as A / B = C / D, cross-multiply to get A × D = B × C, then divide by the number paired with x. For 3 / 12 = x / 30: 12 × x = 3 × 30 = 90, so x = 90 ÷ 12 = 7.5.
How do you know if two ratios are proportional?
Cross-multiply. A : B and C : D are proportional when A × D = B × C. For example, 4 : 6 and 10 : 15 are proportional because 4 × 15 = 60 and 6 × 10 = 60, while 2 : 3 and 5 : 7 are not because 14 ≠ 15.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities rise together and their ratio stays constant (y = kx). In an inverse proportion one rises as the other falls and their product stays constant (y = k / x): 4 workers taking 6 days means 3 workers take 4 × 6 ÷ 3 = 8 days.
Is the rule of three the same as a proportion?
Yes. The rule of three is the name for solving a direct proportion when three values are known: if a corresponds to b, then c corresponds to x = (b × c) ÷ a. It is the same cross-multiplication this calculator performs.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3 : 4. A proportion is an equation stating that two ratios are equal, such as 3 : 4 = 9 : 12. A ratio describes a relationship; a proportion lets you find a missing value when that relationship stays the same.