Ratio Calculator – Simplify & Solve Ratios Online
Simplify ratios and solve ratio problems instantly with our free online ratio calculator. Solve for missing values in proportions and reduce ratios to their simplest form.
Simplify ratios and solve ratio problems instantly with our free online ratio calculator. Solve for missing values in proportions and reduce ratios to their simplest form.
Ratios compare quantities – like ingredients in a recipe, map scales, or aspect ratios for screens. This calculator handles three common tasks: reducing ratios to lowest terms, finding missing values in proportional relationships, and generating equivalent ratios.
Working on homework? The step-by-step solutions show exactly how to simplify using the greatest common divisor, or how to cross-multiply when solving proportions. Understanding the process matters as much as getting the answer.
What is a Ratio?
A ratio compares two quantities by division. It shows how much of one thing exists relative to another.
What is a Proportion?
A proportion states that two ratios are equal. When ratios are proportional, they represent the same relationship.
Simplifying Ratios
Divide both terms by their greatest common divisor (GCD) to get the simplest form.
12 : 18 → GCD is 6 → 2 : 3Solving Proportions
Use cross multiplication: if A/B = C/D, then A × D = B × C. Solve for the unknown.
2/5 = x/15 → 2×15 = 5×x → x = 624 ÷ 12 = 2
36 ÷ 12 = 3
Result: 2 : 3
5x = 8 × 15
5x = 120
x = 24
7 × 4 = 28
Result: 12 : 28
2/3 = x/9
x = (2 × 9) / 3 = 6 cups flour
x = 4.5 × 50000 = 225,000 cm = 2.25 km
Aspect Ratios
Screen dimensions: 16:9 (widescreen), 4:3 (standard), 21:9 (ultrawide). Camera sensors use ratios like 3:2 or 4:3.
Cooking & Baking
Bread: 5:3 flour to water ratio. Pancakes: roughly 2:2:1 flour:milk:eggs. Scale recipes up or down using proportions.
Map Scales
1:24,000 means 1 inch on map = 24,000 inches in reality. Use proportions to convert map distances to real distances.
Mixing Solutions
Concentrate ratios like 1:4 (one part concentrate to four parts water). Maintain ratios when scaling batch sizes.
Financial Ratios
Debt-to-income, price-to-earnings, current ratio. Compare financial health using standardized ratio metrics.
Similar Triangles
Corresponding sides of similar triangles are proportional. Use ratios to find unknown lengths in geometry.
How do I simplify a ratio?
Find the greatest common divisor (GCD) of both numbers, then divide each by the GCD. For 18:24, the GCD is 6, so 18÷6=3 and 24÷6=4, giving 3:4.
What does cross multiplication mean?
In a proportion A/B = C/D, cross multiply means A×D = B×C. This works because you're multiplying both sides by both denominators, eliminating fractions.
Can ratios have decimals?
Yes, but it's often cleaner to convert to whole numbers. Multiply both terms by a power of 10 to eliminate decimals, then simplify. 1.5:2.5 becomes 15:25, which simplifies to 3:5.
What's the difference between a ratio and a fraction?
A fraction represents a part of a whole (3/4 means 3 parts out of 4 total). A ratio compares two separate quantities (3:4 means 3 of one thing for every 4 of another). They're related but conceptually different.
How do I know if two ratios are equivalent?
Simplify both ratios to lowest terms – if they match, they're equivalent. Or cross multiply: if A×D = B×C, then A:B and C:D are equivalent.
Can I simplify ratios with fractions?
Yes. First, find a common denominator for both terms, then treat the numerators as a whole number ratio. For 1/2 : 3/4, convert to 2/4 : 3/4, giving 2:3.
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