The Ratio Calculator simplifies ratios to their lowest terms and helps you solve proportions by finding missing values. It is useful for cooking recipes, mixing solutions, map scales, and any situation where you need to work with proportional relationships.
Enter a ratio to simplify it, or enter three values of a proportion to find the missing fourth value.
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A ratio compares two or more quantities of the same kind. It shows how much of one thing there is compared to another. Ratios can be written as a:b, a/b, or 'a to b'. To simplify a ratio, divide both parts by their greatest common divisor (GCD). For example, 12:8 has GCD 4, so it simplifies to 3:2.
A proportion states that two ratios are equal: a/b = c/d. The cross-multiplication property tells us that a x d = b x c. This is the basis for finding missing values and checking equivalency. If a:b = c:d, then ad = bc.
Multi-term ratios (a:b:c) are simplified by finding the GCD of all terms. Part-to-whole conversion divides each part by the total sum. For a ratio of 3:5, the total is 8, so the parts represent 3/8 (37.5%) and 5/8 (62.5%) of the whole.
Aufgabe: Simplify the ratio 48:36.
Loesung: Find the GCD of 48 and 36. The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCD is 12. Divide both parts: 48/12 = 4, 36/12 = 3.
Antwort: 4:3
Aufgabe: If 5:8 = 20:x, find x.
Loesung: Using cross-multiplication: 5 x x = 8 x 20, so 5x = 160, therefore x = 160/5 = 32.
Antwort: x = 32
Aufgabe: Are the ratios 3:4 and 9:12 equivalent?
Loesung: Cross-multiply: 3 x 12 = 36 and 4 x 9 = 36. Since both products are equal (36 = 36), the ratios are equivalent.
Antwort: Yes, 3:4 = 9:12
Aufgabe: Scale the ratio 2:5 by a factor of 7.
Loesung: Multiply both parts by the scale factor: 2 x 7 = 14, 5 x 7 = 35.
Antwort: 14:35
Aufgabe: Simplify 24:36:60.
Loesung: Find the GCD of all three terms. GCD(24, 36) = 12, GCD(12, 60) = 12. Divide each term by 12: 24/12 = 2, 36/12 = 3, 60/12 = 5.
Antwort: 2:3:5
Aufgabe: Express the ratio 3:5 as percentages of the whole.
Loesung: Total parts = 3 + 5 = 8. First part: 3/8 = 0.375 = 37.5%. Second part: 5/8 = 0.625 = 62.5%.
Antwort: 37.5% and 62.5%
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