Dividieren mit dem Kehrwert
About this app
Die Division als bewegte Formel: Der zweite Bruch klappt zum Kehrwert, aus Geteilt wird Mal, dann wird über Kreuz gekürzt und ausgerechnet. Mit Bruch durch Zahl, Zahl durch Bruch, gemischten Zahlen, der Begründung über den Doppelbruch, zwei typischen Fehlern und einem Übungsmodus.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
Why you multiply by the reciprocal
To divide by a fraction you multiply by its reciprocal. The reciprocal is formed by swapping numerator and denominator: 5/8 becomes 8/5. Only the second fraction, the one you divide by, is flipped. The complex fraction shows why: write 3/4 : 5/8 as one fraction with 3/4 on top and 5/8 below, then multiply top and bottom by 8/5. The bottom becomes 5/8 · 8/5 = 1, and 3/4 · 8/5 remains.
What the app shows
The calculation is shown as a large formula in the centre. The second fraction visibly flips around its fraction bar and the division sign turns into a multiplication dot. Then it continues as with multiplying: everything on one fraction bar, cancel diagonally, multiply. So 3/4 : 5/8 becomes 6/5 = 1 1/5. Fraction by number (3/4 : 3 = 1/4), number by fraction (3 : 1/2 = 6) and mixed numbers (1 1/2 : 3/4 = 2) are included. Below the formula one sentence explains each step.
Try it yourself
Set your own tasks with large plus and minus buttons and step forwards and backwards. The method “First flipped?” shows the most common mistake: 4/3 · 5/8 gives 5/6, exactly the reciprocal of the correct result; the check settles it. The method “Top : top?” shows that dividing numerator by numerator only works when both divisions work out. In practice mode you tap the fraction to flip, enter the reciprocal and cancel yourself.
Frequently asked questions
- Which fraction do you flip when dividing?
- Only the second fraction, the divisor. The first fraction stays, and divide becomes multiply: 3/4 : 5/8 = 3/4 · 8/5. Flipping the first fraction gives exactly the reciprocal of the correct result.
- Why may you multiply by the reciprocal?
- Write the division as a complex fraction and multiply top and bottom by the reciprocal of the divisor. The bottom becomes 1, because a fraction times its reciprocal is always 1. The top is the first fraction times the reciprocal.
- How do you divide a whole number by a fraction?
- Write the number as a fraction with denominator 1 and multiply by the reciprocal: 3 : 1/2 = 3/1 · 2/1 = 6. Dividing by a fraction less than 1 makes the result larger.
- What can I try in the app?
- Your own tasks with numbers up to 12, four task types, the reason via the complex fraction, the mistakes “first fraction flipped” and “top by top”, and a practice mode for flipping and cancelling.
Subject: Bruchrechnung (Klasse 6)
More from Bruchrechnung (Klasse 6)
- Bruch-Werkstatt: Was ein Bruch bedeutet
- Brüche addieren und subtrahieren
- Brüche als Dezimalzahl und Prozent
- Brüche dividieren: Wie oft passt es hinein?
- Brüche multiplizieren mit kreuzweisem Kürzen
- Brüche multiplizieren: Anteil vom Anteil
- Brüche vergleichen und ordnen
- Bruchteile von Mengen und Größen
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