Ratio Calculator

Frequently Asked Questions

How do I simplify a ratio?

Divide both terms by their GCD. So 18:24 simplifies to 3:4 because GCD(18, 24) = 6.

How do I solve a proportion?

Cross multiply: a/b = c/d means a × d = b × c. So x/4 = 6/8 gives 8x = 24, so x = 3.

What is the difference between a ratio and a fraction?

A fraction compares part to whole; a ratio compares part to part. The ratio 1:2 means the second is twice the first; as a fraction of the total it is 1/3.

Where are ratios used in real life?

Recipe scaling, mixing concrete, financial ratios like P/E, map scales, gear ratios, and screen aspect ratios all rely on this concept.

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How This Calculator Works

The calculator has three modes. Simplify divides both parts of a ratio a:b by their greatest common divisor (GCD) to produce the simplest equivalent ratio. Solve proportion finds the missing value x in a:b = c:x using cross-multiplication: x = (b × c) / a. Scale ratio multiplies both parts of a:b by a given scale factor.

Understanding Ratios

A ratio compares two quantities of the same kind, written as a:b or a/b. Ratios can represent part-to-part relationships (boys to girls in a class) or part-to-whole relationships (boys to all students). A ratio of 3:4 is equivalent to 6:8, 9:12, and 0.75 - these all describe the same proportional relationship.

Key Concepts

Simplifying with GCD: To reduce 18:24, find GCD(18,24) = 6, then divide both sides: 3:4. A simplified ratio uses the smallest possible whole numbers.

Proportions & cross-multiplication: If a/b = c/d, then ad = bc. This allows solving for any one unknown given the other three values. Used constantly in unit conversions, map scales, and recipe scaling.

Unit rate: A ratio where the second term equals 1. Example: 300 miles in 5 hours = 60 miles per hour (60:1). Unit rates make comparisons between different quantities straightforward.

Golden ratio (φ ≈ 1.618): The ratio a:b where (a+b)/a = a/b. It appears in the Fibonacci sequence, Renaissance art, nautilus shells, and architectural proportions. Rectangles with this ratio are perceived as especially pleasing.

Aspect ratios: Screen and image dimensions are expressed as ratios. HD video is 16:9 (1.78:1); classic film is 4:3 (1.33:1); IMAX is approximately 1.43:1.

Everyday Ratio Applications

Recipe scaling: A recipe for 4 serves using 2 cups flour - scaling to 10 servings: 2/4 = x/10, so x = 5 cups.

Map scales: A map scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in reality.

Concrete mixing: A standard mix ratio is 1:2:3 (cement:sand:aggregate) by volume.

Fuel mixtures: Two-stroke engines require oil:fuel ratios like 1:50 for proper lubrication.

Ratio Calculator

Frequently Asked Questions

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