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Proportionsrechner | Verhältnisse per Kreuzprodukt lösen

a/b = c/d für jeden fehlenden Wert per Kreuzprodukt lösen. Unbekannte Zähler oder Nenner finden und äquivalente Verhältnisse prüfen. Kostenloser Proportionsrechner.

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Mathematik-Rechner

Proportionsrechner

a / b = c / d
Solved value (d)
8
Linkes Verhältnis (a÷b)0.75
Rechtes Verhältnis (c÷d)0.75
Als Prozent (a/b)75%

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What Is a Proportion Calculator?

A proportion states that two ratios are equal — like 3/4 = 6/8. This free proportion calculator uses cross-multiplication to find any missing numerator or denominator in a/b = c/d, and shows both ratios as decimals and percentages.

How to Use This Calculator

  1. Select which value is unknown (a, b, c, or d).
  2. Enter the three known values in the proportion fields.
  3. Read the solved value and ratio comparison in the results panel.
  4. Check the percentage equivalent for the left ratio.

Proportion Formula

a × d = b × c
  • a, c = numerators (top values)
  • b, d = denominators (bottom values)
  • To solve for d: d = (b × c) / a

Worked Example

Solve 3/4 = 6/d. Cross-multiply: 3 × d = 4 × 6, so 3d = 24, and d = 8. Check: 3/4 = 0.75 and 6/8 = 0.75 — the proportion holds.

Common Use Cases

  • Scaling recipe ingredients up or down
  • Kartenmaßstäbe in reale Maße umrechnen
  • Solving algebra homework with missing numerators or denominators

Frequently Asked Questions (FAQs)

How do you solve a proportion?

For a/b = c/d, cross-multiply: a × d = b × c. Then isolate the unknown. If x/b = c/d, then x = (b × c) / d.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (like 3:4). A proportion states that two ratios are equal (like 3/4 = 6/8).

Can this calculator find any missing value?

Yes. Choose which of a, b, c, or d is unknown and enter the other three — the tool solves via cross-multiplication.

What is cross-multiplication?

Cross-multiplication sets a × d equal to b × c. In a true proportion, both products are identical.

How do you solve 3/4 = x/8?

Cross-multiply: 3 × 8 = 4 × x, so 24 = 4x, and x = 6. The proportion 3/4 = 6/8 is correct.

What happens if a denominator is zero?

Division by zero is undefined. The calculator shows an error instead of returning a result when a denominator would be zero.