How do I simplify a ratio to its lowest terms?
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers, then divide both numbers by the GCD. For example, to simplify 12:18, the GCD is 6, so 12÷6:18÷6 = 2:3.
What's the difference between a ratio and a fraction?
A ratio compares two or more quantities (A:B), while a fraction represents a part of a whole (A/B). Ratios can be written as fractions, but they serve different purposes. A ratio shows relative sizes, while a fraction shows division.
How do I convert a ratio to a percentage?
To convert a ratio to percentages, first add both numbers to get the total. Then divide each number by the total and multiply by 100. For example, 3:2 becomes: 3/(3+2)×100 = 60% and 2/(3+2)×100 = 40%.
Can ratios have more than two numbers?
Yes, ratios can compare three or more quantities (e.g., 2:3:5). This calculator focuses on two-number ratios, but the same principles apply. To simplify multi-number ratios, divide all numbers by their GCD.
What is a proportion problem?
A proportion problem involves finding a missing value when two ratios are equal. For example: if 4:6 = x:9, find x. Use cross-multiplication: (4×9)/6 = 6. This is commonly used in scaling recipes, map scales, and currency conversion.
What are equivalent ratios?
Equivalent ratios represent the same relationship even though the numbers are different. For example, 1:2, 2:4, 3:6, and 50:100 are all equivalent ratios. They all simplify to 1:2.
How do I scale a ratio up or down?
To scale a ratio, multiply (to increase) or divide (to decrease) both numbers by the same factor. For example, to double 3:5, multiply both by 2 to get 6:10. To halve it, divide both by 2 to get 1.5:2.5.
What is the golden ratio?
The golden ratio, approximately 1.618:1 (or φ:1), is a special ratio found in nature, art, and architecture. It's considered aesthetically pleasing and appears in the proportions of the Parthenon, Renaissance paintings, and even in spiral patterns of shells and galaxies.