Solve missing ratio values, simplify ratios to their lowest terms, scale aspect ratios like 16:9, or split an amount by ratio.
Solves equivalent fractions A/B = C/X by cross-multiplying: X = (B × C) / A.
Finds the Greatest Common Divisor (GCD) of multi-part ratios to simplify terms to integers.
Resizes image and video dimensions (e.g. 16:9, 4:3) maintaining identical visual proportions.
Splits a monetary sum or quantity proportionally across multiple ratio shares: Share_A = Total × (A / Sum).
Fundamental mathematical relationships to solve proportions, simplify multi-part terms, scale visual aspect ratios, and partition monetary amounts:
A ratio compares the relative sizes of two or more values. Expressed as A:B, A/B, or "A to B", it indicates how many times one number contains another.
A proportion states two ratios are equal (A:B = C:D). When 3 values are known, target X is computed via cross-multiplication: X = (B × C) ÷ A.
Ratios simplify by dividing all terms by their Greatest Common Divisor (GCD). E.g., 12:18:24 simplifies to 2:3:4 when divided by 6.
Scale recipe quantities proportionally when modifying batch yields without disturbing flavor balance.
Convert blueprint scale ratios (e.g. 1:50, 1:100) into actual building measurements accurately.
Maintain 16:9, 4:3, or 21:9 image and monitor aspect ratios to avoid stretching or letterboxing distortion.
Evaluate leverage metrics like Debt-to-Equity (D/E), equity partnership splits, and profit margins.
A proportion A:B = C:X is solved by cross-multiplication: A x X = B x C, so X = (B x C) / A. For example, in 2:3 = 10:X, X = (3 x 10) / 2 = 15.
A ratio is simplified to its lowest terms by dividing every term by their greatest common divisor (GCD). The ratio 4:6 has a GCD of 2, so it simplifies to 2:3, and this same GCD method extends to three-term ratios such as 4:6:8, which simplifies to 2:3:4.
To split a total amount by a ratio such as 2:3:5, add the parts together (2 + 3 + 5 = 10 parts) and divide the total by that sum to find the value of one part. For a total of 1,000 split 2:3:5, one part equals 100, giving shares of 200, 300, and 500.
Use the Fraction Calculator when a ratio needs to be added to or compared against a fraction, and the LCM & HCF Calculator when you need the underlying common divisor or multiple used to simplify or scale a ratio.
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