Ratio and proportion formulas
Simplify: A : B = (A ÷ gcd) : (B ÷ gcd)
Proportion: A : B = C : D → D = B × C ÷ A
Proportion: A : B = C : D → D = B × C ÷ A
Example 1 — proportion: A recipe uses 3 cups of flour for 4 eggs. For 12 cups of flour you need 4 × 12 ÷ 3 = 16 eggs.
Example 2 — simplify: A 1920 × 1080 screen has a ratio of 1920 : 1080. The GCD is 120, so it simplifies to 16 : 9.
Example 2 — simplify: A 1920 × 1080 screen has a ratio of 1920 : 1080. The GCD is 120, so it simplifies to 16 : 9.
Common uses of ratios
- Scaling recipes up or down while keeping flavors balanced.
- Mixing concrete, fuel, fertilizer, paint or cleaning solutions.
- Maps and models — a 1:25,000 map means 1 cm equals 250 m.
- Aspect ratios for photos, video and displays (4:3, 16:9, 21:9).
Frequently asked questions
How do you simplify a ratio?
Divide both parts by their greatest common divisor. For 1920:1080 the GCD is 120, giving 16:9. If the ratio contains decimals, multiply both parts by 10, 100, etc. first to make them whole numbers.
How do you solve a proportion?
Cross-multiply. For A:B = C:D, D = B × C ÷ A. If 3 cups of flour need 4 eggs, 12 cups need 4 × 12 ÷ 3 = 16 eggs.
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole (3 of 4 parts = 3/4). A ratio can compare any two quantities, including part to part: in a 3:1 mix, the paint is 3/4 of the total and the thinner 1/4.
How do I convert a ratio to a percentage?
Add the parts to get the total, then divide each part by the total. In a 3:2 ratio, the first part is 3 ÷ 5 = 60% and the second 40%.