Kürzen Schritt für Schritt
About this app
Kürzen als bewegte Formel: in Etappen mit Bögen „: 2“ an Zähler und Nenner oder in einem Schritt mit dem ggT, wenn gemeinsame Primfaktoren paarweise gestrichen werden. Mit Erweitern als Rückweg, der Summen-Falle samt Probe und Übungen zum Teiler-Wählen und Faktoren-Streichen.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
What simplifying means
To simplify a fraction you divide numerator and denominator by the same number. The share stays the same, only the numbers get smaller: 36/48 and 3/4 describe the same piece. A fraction is in lowest terms when numerator and denominator have no common factor other than 1. You can simplify in stages, for example by 2, by 2 again and then by 3, or in one step by the greatest common factor, the GCF. Expanding is the way back: numerator and denominator are multiplied by the same number.
What the app shows
The calculation is shown as a large formula in the centre and moves step by step. In the method “In stages” the chain 36/48 = 18/24 = 9/12 = 3/4 appears, with arcs at numerator and denominator showing the divisor. In the method “With the GCF”, 36 = 2 · 2 · 3 · 3 and 48 = 2 · 2 · 2 · 2 · 3 are broken down, equal factors on top and below are joined as pairs and crossed out, leaving 3/4. The method “Expand” leads from 3/4 back to 36/48. Below each step one sentence explains it.
Try it yourself
Set numerator and denominator up to 99 with large plus and minus buttons or ask for a new task, and play the calculation forwards and backwards. The method “Sums?” shows a common trap: in (3 + 6)/(3 + 9) the 3 must not be crossed out; the check gives 3/4 against 2/3. In the Practice panel you choose factors yourself and recognise when the fraction is in lowest terms, or you tap equal prime factors on top and below to cross them out.
Frequently asked questions
- How do you simplify a fraction fully?
- Divide numerator and denominator by their greatest common factor, the GCF. For 36/48 the GCF is 12, so 36 : 12 = 3 and 48 : 12 = 4. Alternatively simplify in stages until numerator and denominator have no common factor other than 1.
- How do you find the GCF of two numbers?
- With prime factors: 36 = 2 · 2 · 3 · 3 and 48 = 2 · 2 · 2 · 2 · 3. The product of the common factors 2 · 2 · 3 = 12 is the GCF. Or with lists of factors: write down all factors of both numbers and look for the greatest common one.
- Can you cancel parts of a sum?
- No. In (3 + 6)/(3 + 9) the 3 must not be crossed out, because simplifying means dividing the whole numerator and the whole denominator. Correct is 9/12 = 3/4; crossing out would give 6/9 = 2/3.
- What can I try in the app?
- Simplify your own fractions with numbers up to 99, step forwards and backwards through the methods “In stages”, “With the GCF”, “Expand” and “Sums?”, and in practice mode choose factors or cross out common prime factors.
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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