Hauptnenner bilden und Brüche addieren
About this app
Die Rechnung als bewegte Formel: Hauptnenner über Vielfachenreihen, Primfaktoren oder das Produkt der Nenner finden, mit Bögen erweitern, gleichnamig addieren, kürzen und als gemischte Zahl schreiben. Mit Minus, drei Brüchen, der Falle „Nenner addieren“ samt Probe 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.
What the lowest common denominator is
Fractions with different denominators can only be added or subtracted once the pieces have the same size. To get there, you expand all fractions to a common denominator. The smallest one is the lowest common denominator, the least common multiple (lcm) of the denominators. For 5/6 + 3/8 it is 24: in the rows 6, 12, 18, 24 and 8, 16, 24, 24 is the first number in both. Prime factors work too: 6 = 2 · 3, 8 = 2 · 2 · 2, so lcm = 2 · 2 · 2 · 3 = 24.
What the app shows
The calculation is a large formula in the centre, and every step moves: the rows of multiples appear one below the other and the first common number lights up. Below the fractions the expansion factors 24 : 6 = 4 and 24 : 8 = 3 appear, and arcs “· 4” and “· 3” show that numerator and denominator are multiplied by the same number. Then the numerators move together onto one fraction bar: 20/24 + 9/24 = 29/24 = 1 5/24. A short sentence explains why each step is allowed.
Try it yourself
Set your own tasks with plus, minus or three fractions, for example 1/2 + 1/3 + 1/4. Compare the methods: rows of multiples, prime factors, or simply the product of the denominators, which also works but gives bigger numbers and has to be simplified at the end. The method “Add denominators?” shows the most common mistake: 5/6 + 3/8 is not 8/14, because 8/14 would be even smaller than 5/6 alone. In practice mode you choose the common denominator, the factors and the result yourself.
Frequently asked questions
- How do you find the lowest common denominator of two fractions?
- Look for the least common multiple of the denominators. Either list the multiples of both denominators until a number appears in both lists, or split the denominators into prime factors and take each factor as often as it appears at most.
- Why can you not add the denominators when adding fractions?
- The denominator tells you the size of the pieces; only the pieces, the numerators, are added. Working out 5/6 + 3/8 = 8/14 would give a result smaller than 5/6 alone, which cannot happen when adding.
- Can you use the product of the denominators as the common denominator?
- Yes, the product is always a common denominator. For 6 and 8 it is 48 instead of 24. The result 58/48 then has to be simplified by 2, which again gives 29/24.
- What can I try in the app?
- Set your own tasks with numerators up to 12, work with plus, minus and three fractions, compare the methods multiples, prime factors and product, look at the trap “adding the denominators” with its check, and choose the common denominator, factors and result yourself in practice mode.
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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