Solve proportions A:B = C:D, simplify multi-part ratios to lowest terms, and divide an amount or quantity by given ratio shares.
In a proportion A/B = C/D, the product of extremes equals the product of means.
A ratio expresses the proportional relationship between two or more numbers, indicating how many times one value contains or relates to another (e.g. A : B). A proportion states that two ratios are exactly equivalent (A : B = C : D). Ratios are foundational to cooking recipes, currency exchange, map scales, screen aspect ratios, and financial metrics.
In any true proportion A/B = C/D, the cross-products are equal: A · D = B · C. If one value is unknown (e.g., D = x), then x = (B · C) / A.
A ratio A : B : C can be simplified to lowest terms by dividing all terms by their Greatest Common Divisor: GCD(A, B, C).
To divide an amount into ratio parts A : B : C, add the parts (A + B + C), find the unit value = Total / Sum, and multiply by each part.
Standard widescreen display aspect ratios (such as 16:9 or 21:9) describe the width-to-height proportion regardless of absolute pixel resolution.
Solve 3 : 5 = 12 : x, and divide $1,000 profit between two partners in ratio 3 : 2.
A fraction typically represents a part-to-whole relationship (e.g. 3 slices out of 8 is 3/8). A ratio can represent either part-to-part (3 boys to 5 girls) or part-to-whole (3 boys to 8 total students).
Ratios usually compare non-negative quantities. If numbers contain decimals (e.g. 1.5 : 2.5), multiply by 10 to get 15 : 25, then simplify to 3 : 5.
The Golden Ratio is an irrational constant φ = (1 + √5) / 2 ≈ 1.6180339887... Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity.
A map scale of 1 : 50,000 means 1 unit on the map represents 50,000 of the same units in real life (e.g. 1 cm on the map equals 50,000 cm or 500 meters in reality).
Understanding your calculation
A ratio compares quantities in a specified order. Integer ratios simplify by dividing each term by their greatest common factor.
12:18 reduces to 2:3. Keeping the same relationship, a first quantity of 10 corresponds to a second quantity of 15.
Keep units and the order of quantities consistent. A part-to-part ratio is different from a part-to-total percentage.