Simplify ratios using GCD and solve proportions like a:b = c:?. Free online ratio simplifier and proportion solver for math, cooking, and design.
The Ratio Calculator simplifies any ratio to its lowest terms and solves proportional relationships. Enter two numbers to simplify the ratio using the Greatest Common Divisor, or enter three values to solve for the missing fourth in a proportion.
Ratios express the relationship between two quantities. A ratio of 12:8 simplifies to 3:2, meaning for every 3 units of one quantity there are 2 of the other. This simplification makes ratios easier to understand and compare.
Ratios are used in cooking (ingredient proportions), design (aspect ratios like 16:9), finance (debt-to-income ratios), science (molar ratios), and construction (mix ratios for concrete). This calculator handles all these scenarios with precision.
Quantifying this parameter enables meaningful comparison across time periods and projects, revealing trends that inform better decisions about personal productivity and resource management. This structured approach transforms vague productivity goals into measurable targets, making it easier to track improvement and stay motivated toward meaningful professional achievements.
Simplifying ratios by hand requires finding the GCD, which is tedious for large numbers. Solving proportions (a:b = c:?) requires cross-multiplication. This tool does both instantly. Data-driven tracking enables proactive schedule management, helping professionals protect focused work time and reduce the cognitive overhead of constant task-switching throughout the day. This quantitative approach replaces vague time estimates with concrete data, enabling professionals to plan realistic schedules and avoid the pattern of chronic overcommitment.
Simplified Ratio: A/GCD(A,B) : B/GCD(A,B) Proportion: if A:B = C:X, then X = (B × C) / A
Result: Simplified: 2:3, Missing value: 15
GCD(24,36) = 12. Simplified: 24/12 : 36/12 = 2:3. For 2:3 = 10:?, cross-multiply: ? = (3 × 10) / 2 = 15.
Ratios simplify complex relationships. Instead of saying "for 300ml of A, use 200ml of B," you can say "3:2 ratio." This makes scaling intuitive: for 600ml of A, use 400ml of B.
Multiplying or dividing both parts of a ratio by the same number produces an equivalent ratio. 2:3 is the same as 4:6, 6:9, or 1:1.5. Simplification finds the smallest whole-number equivalent.
Businesses track dozens of ratios: debt-to-equity, current ratio, quick ratio, and inventory turnover. Each ratio distills complex financial data into a simple comparison, enabling quick decision-making.
Divide both numbers by their Greatest Common Divisor (GCD). For 18:24, GCD is 6, so the simplified ratio is 3:4.
A proportion states that two ratios are equal: a/b = c/d. If you know three of the four values, you can solve for the missing one using cross-multiplication.
Yes, though they are typically expressed as whole numbers. A ratio of 2.5:5 can be multiplied by 2 to get 5:10, then simplified to 1:2.
The golden ratio is approximately 1:1.618 (or φ). It appears in nature, art, and architecture and is considered aesthetically pleasing.
Recipes use ratios for consistent results regardless of batch size. A 3:1 flour-to-sugar ratio scales perfectly whether making 1 cake or 10.
An aspect ratio describes the proportional relationship between width and height. Common screen aspect ratios include 16:9 for widescreen and 4:3 for traditional displays.