Brüche addieren und subtrahieren
About this app
Zwei Bruchstreifen werden gleichnamig gemacht: Neue Schnittlinien teilen jedes Stück, bis alle Stücke den Hauptnenner haben, dann fliegen sie in den Ergebnisstreifen (bzw. werden weggenommen), am Ende wird gekürzt, über 1 als gemischte Zahl. Der Knopf „Typischer Fehler“ widerlegt 1/2 + 1/3 = 2/5: 2/5 ist sogar kleiner als 1/2 allein. Mit Übungsaufgaben und Rückmeldung an der Szene.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
Why fractions need a common denominator
You can only count pieces of the same size together. If two fractions have the same denominator, add the numerators and keep the denominator: 1/5 + 2/5 = 3/5. If the denominators differ, expand both fractions to a common denominator, most simply the lowest common denominator, the least common multiple of the denominators. For 1/2 + 1/3 that is 6: 3/6 + 2/6 = 5/6. Subtracting works the same way. Finally you simplify, and a result above 1 is often written as a mixed number.
What the app shows
Two strips stand for the two fractions, below them is the result strip with the scale 0, 1, 2. In the step Common denominator new cut lines grow into every piece until both strips have equally fine fields; a grid links them. Then the pieces fly into the result strip; when subtracting, the pieces of the second fraction land on the end of the first and vanish with them. When simplifying, the joints between the pieces close. On the left each fraction is stacked, at the bottom the working.
Try it yourself
Tap into a strip to choose the numerator and set the denominators from 1 to 12. The button Common mistake adds numerator plus numerator and denominator plus denominator: 1/2 + 1/3 gives 2/5, and a line shows that 2/5 is even smaller than 1/2 alone. The Practise panel gives you random tasks. The feedback shows the correct way in the scene and marks where your answer lies.
Frequently asked questions
- How do you add fractions with different denominators?
- Expand both fractions to a common denominator, ideally the lowest common denominator, the least common multiple of the denominators. Then add the numerators and keep the denominator. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- Why is 1/2 + 1/3 not 2/5?
- Because halves and thirds are pieces of different sizes, so you cannot simply count them. 2/5 is even smaller than 1/2 alone, although 1/3 is added. The correct result is 5/6.
- When do you have to simplify the result?
- When numerator and denominator share a divisor greater than 1. For example 1/6 + 2/6 = 3/6, and 3/6 simplifies by 3 to 1/2. If the result is greater than 1, it is often written as a mixed number: 17/12 = 1 5/12.
- What can I try in the app?
- Add and subtract fractions with denominators up to 12, view each step on its own (show, common denominator, push together, simplify), disprove the mistake ½ + ⅓ = 2/5 and solve practice tasks with instant feedback.
Subject: Bruchrechnung (Klasse 6)
More from Bruchrechnung (Klasse 6)
- Bruch-Werkstatt: Was ein Bruch bedeutet
- 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
- Dividieren mit dem Kehrwert
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