Brüche multiplizieren mit kreuzweisem Kürzen
About this app
Die Rechnung als bewegte Formel: Beide Brüche wandern auf einen Bruchstrich, Zahlen über Kreuz werden gekürzt, erst dann wird ausgerechnet. Mit Zahl mal Bruch, dem Vergleich „erst ausrechnen“, der Plus-Falle und einem Übungsmodus zum Antippen.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
Why you may cancel diagonally
To multiply two fractions you multiply numerator by numerator and denominator by denominator. Writing this on one common fraction bar first gives a single fraction, for example (3 · 8)/(4 · 9). In that fraction any number in the numerator may be cancelled with any number in the denominator, including the numbers that sit diagonally in the task: 3 with 9 and 8 with 4. Cancelling before multiplying keeps the numbers small, and the result is in lowest terms straight away.
What the app shows
The calculation is shown as a large formula in the centre. At each step the numbers glide to their new place: the two fraction bars grow into one, the diagonal pairs are highlighted, cancel strokes are drawn and the new small numbers move in. Below the formula one sentence explains each step. Number times fraction is included too: 4 · 3/8 becomes 4/1 · 3/8, and the result 3/2 appears as the mixed number 1 1/2.
Try it yourself
Set numerators and denominators with large plus and minus buttons or ask for a new task. Compare the method “Multiply first”: 3/4 · 8/9 becomes 24/36 and you have to cancel by 12. The method “With plus?” shows why you may not cancel diagonally in 3/4 + 8/9: the check with the common denominator gives different values. In practice mode you tap two diagonal numbers yourself, choose the factor and see the cancel strokes on the formula.
Frequently asked questions
- When may you cross-cancel fractions?
- Only when multiplying (and when dividing, after multiplying by the reciprocal). Then all numerators and denominators are on one fraction bar, and any number on top may be cancelled with any number below.
- Can you cross-cancel when adding fractions?
- No. In 3/4 + 8/9 there are two fractions side by side without a common fraction bar. Cancelling 3 and 9 anyway gives 1/4 + 8/3 = 35/12, while the correct sum is 59/36.
- How do you multiply a whole number by a fraction?
- Write the number as a fraction with denominator 1 and multiply as usual. The number only goes into the numerator: 4 · 3/8 = (4 · 3)/8 = 12/8 = 3/2.
- What can I try in the app?
- Set your own tasks with numbers up to 12, step forwards and backwards through the calculation, compare the methods “Cancel first”, “Multiply first” and “With plus?”, and cancel diagonal pairs 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: Anteil vom Anteil
- Brüche vergleichen und ordnen
- Bruchteile von Mengen und Größen
- Dividieren mit dem Kehrwert
A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps