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Bruchrechner für Brüche und Doppelbrüche

Dieser Bruchrechner addiert, subtrahiert, multipliziert und dividiert Brüche — auch einen Bruch durch einen Bruch — und gibt das Ergebnis vollständig gekürzt und als gemischte Zahl an, z. B. 17/5 = 3 2/5.

Brüche wie 3/4, ganze Zahlen oder Dezimalzahlen

Ergebnis

Gib Werte ein und tippe auf Berechnen, um das Ergebnis zu sehen.

Formel

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

To add or subtract, rewrite both fractions over a common denominator first.

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Dividing by a fraction is the same as multiplying by its reciprocal.

So benutzt du diesen Rechner

  1. Type each fraction with a slash, e.g. 3/4. Whole numbers and decimals work too.
  2. Choose the operation and press Calculate.
  3. For improper results you also get a mixed number, e.g. 7/3 = 2 1/3.
  4. For a complex fraction such as (3/4)/(5/8), choose ÷ and enter 3/4 and 5/8.
  5. Adding fractions with variables works the same way by hand: x/2 + x/3 = 3x/6 + 2x/6 = 5x/6.
  6. To factor a fraction out of an expression, divide each term by it: ½x + ¼ = ¼(2x + 1).

Gelöste Beispiele

Add 1/2 and 1/3

The least common denominator of 2 and 3 is 6.

1/2 = 3/6 and 1/3 = 2/6, so the sum is 5/6.

Medium: a complex fraction

The complex fraction (3/4)/(5/8) means 3/4 ÷ 5/8.

Multiply by the reciprocal: 3/4 × 8/5 = 24/20.

Simplify by 4: 24/20 = 6/5, or 1 1/5 as a mixed number.

Hard: negative mixed numbers

−2 1/3 = −7/3. Multiply: −7/3 × 9/14 = −63/42.

Simplify by 21 (or cancel 7 with 14 and 3 with 9 first): −3/2 = −1 1/2.

Häufige Fehler

  • Adding the denominators: 1/2 + 1/3 is 5/6, not 2/5. Use a common denominator first.
  • Dividing straight across: 3/4 ÷ 5/8 means multiplying by the reciprocal 8/5, giving 6/5.
  • Forgetting to simplify: 24/20 should be written as 6/5.
  • Mixed number errors: 17/5 is 3 2/5, because 5 × 3 = 15 and 17 − 15 = 2.

Häufig gestellte Fragen

How do I simplify a complex fraction?

A complex fraction has a fraction on top and/or bottom. Rewrite it as a division and multiply by the reciprocal: (3/4)/(5/8) = 3/4 × 8/5 = 6/5.

What is 17/5 as a mixed number?

3 2/5. Five goes into 17 three times (15) with 2 left over.

Is this a rational numbers calculator?

Yes. Fractions, whole numbers and terminating decimals are all rational numbers, and the calculator keeps every result exact as a fraction.

How do I enter a mixed number like 2 1/3?

Convert it to an improper fraction first: 2 1/3 = 7/3. The answer shows mixed numbers for you.

Is the answer simplified?

Yes. Results are always reduced to lowest terms by dividing by the greatest common divisor.

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