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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.

Ratio Calculator
Simplify ratios, solve proportions, and find equivalent ratios.
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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.

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.

Understanding Ratios and Proportions

What is a Ratio?

A ratio compares two quantities by division. It shows how much of one thing exists relative to another.

Notation: A : B or A/B or "A to B"
Example: 3 : 4 means 3 parts to 4 parts
Real use: Recipe ratios, map scales, screen dimensions

What is a Proportion?

A proportion states that two ratios are equal. When ratios are proportional, they represent the same relationship.

Notation: A : B = C : D
Cross product: A × D = B × C
Use: Scale drawings, similar triangles, unit conversions

Simplifying Ratios

Divide both terms by their greatest common divisor (GCD) to get the simplest form.

12 : 18 → GCD is 6 → 2 : 3

Solving 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 = 6
Ratio Examples
Simplify 24 : 36
GCD(24, 36) = 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Result: 2 : 3
Solve: 5 : 8 = 15 : x
5/8 = 15/x
5x = 8 × 15
5x = 120
x = 24
Find equivalent of 3 : 7 multiplied by 4
3 × 4 = 12
7 × 4 = 28
Result: 12 : 28
Recipe: 2 cups flour for 3 cups sugar. How much flour for 9 cups sugar?
2 : 3 = x : 9
2/3 = x/9
x = (2 × 9) / 3 = 6 cups flour
Map scale 1 : 50,000. What's the real distance if map shows 4.5 cm?
1 : 50000 = 4.5 : x
x = 4.5 × 50000 = 225,000 cm = 2.25 km
Common Ratio Applications

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.

Frequently Asked Questions

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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