Brüche dividieren: Wie oft passt es hinein?
About this app
Messstück anlegen und zählen, wie oft es in den Streifen passt, auch mit Reststück als Bruchteil; Verteilen durch eine natürliche Zahl; die Kehrwertregel aus der Eins-Reihe; Zahlenstrahl zeigt, wann Teilen größer macht.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
What dividing by a fraction means
The task 3 : 1/2 asks how many times a half fits into 3 wholes. The answer is 6, which is more than 3. Dividing here means measuring. If the measuring piece does not fit exactly, the remainder is a part of the measuring piece: for 3/4 : 1/2 the half fits once completely, 1/4 is left, and that is half of the measuring piece. So 3/4 : 1/2 = 1 1/2. To divide by a fraction, multiply by its reciprocal: 3/4 · 2/1 = 6/4 = 1 1/2. Dividing by a whole number means sharing: 4/5 : 2 = 2/5.
What the app shows
Chocolate bars stand for the wholes, and the filled pieces in the course colour are the first fraction. Below, the measuring piece in the contrast colour is laid along one piece at a time, count marks keep track, and a dashed overhang shows what no longer fits. New cut lines make the remainder countable. A one-row lays the measuring piece into a single whole and so shows the reciprocal. A number line uses an arc to show whether the result is greater or less than the first number, and the calculation flips the divisor card.
Try it yourself
Set numerator and denominator with large plus and minus fields or drag the handles of the strip and the measuring piece. Compare 3 : 1/2 with 3 : 2 and see when dividing makes things greater. For 3/4 : 1/2, show the mistake of flipping the wrong fraction: 4/3 · 1/2 = 2/3 would be too small. In sharing mode, divide 3/4 by 2 and watch every quarter being halved. The practice panel has short tasks with feedback right in the scene.
Frequently asked questions
- How do you divide two fractions?
- Multiply the first fraction by the reciprocal of the second. In the reciprocal, numerator and denominator swap places: 3/4 : 1/2 = 3/4 · 2/1 = 6/4 = 1 1/2. Only the fraction you divide by is flipped.
- Why does dividing by a fraction make the result bigger?
- Division asks how many times the divisor fits. If it is less than 1, it fits more often than the first number is big. That is why 3 : 1/2 = 6. Dividing by a number greater than 1 makes the result smaller.
- How do you divide a fraction by a whole number?
- Share the fraction into equal parts by multiplying the denominator by the number: 3/4 : 2 = 3/8. If the numerator divides evenly, 4/5 : 2 = 2/5 works too. This is the same as multiplying by the reciprocal 1/2.
- What can I try in the app?
- Set fractions or drag the handles, lay the measuring piece along one by one, count the remainder with the common grid, show the reciprocal rule and the mistake of flipping the wrong fraction, split a fraction in sharing mode and solve short practice tasks.
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 multiplizieren mit kreuzweisem Kürzen
- Brüche multiplizieren: Anteil vom Anteil
- Brüche vergleichen und ordnen
- Bruchteile von Mengen und Größen
- Dividieren mit dem Kehrwert
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