Ratio Calculator Guide: Ratios, Proportions & Cross-Multiplication
Ratios and proportions are fundamental in finance, cooking, construction, and science. Master the key techniques and you'll solve most ratio problems in seconds.
Solving Proportions: Cross-Multiplication
Unknown = (known product) ÷ (opposite known)
Real-World Ratio Applications
Frequently Asked Questions
What is a ratio?
A ratio compares two or more quantities showing how many times one contains the other. Written as A:B or A/B. For example, a ratio of 3:5 means for every 3 of A, there are 5 of B. Ratios are used in maps, recipes, finance, and scale models.
How do I solve a proportion (A:B = C:D)?
Cross-multiply to find the missing value. If A:B = C:D, then A×D = B×C. For example, 3:5 = X:20 → 3×20 = 5×X → X = 60÷5 = 12.
How do I simplify a ratio?
Divide both parts by their Greatest Common Divisor (GCD). For 24:36: GCD is 12. Simplified: 2:3. For 15:25:30: GCD is 5. Simplified: 3:5:6.
What is a direct proportion?
In direct proportion, when one quantity increases, the other increases proportionally. If 5 workers complete a job in 8 hours, 10 workers (double) complete it in 4 hours (half). Written as A ∝ B or A = kB.
What is an inverse proportion?
In inverse proportion, when one quantity increases, the other decreases proportionally. More workers = less time to finish a job. If 4 workers take 12 days, 6 workers take 12 × (4÷6) = 8 days.
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