Gemischte Zahlen umwandeln und rechnen
About this app
Die Rechnung als bewegte Formel: In 2 3/4 taucht das unsichtbare Plus auf, die Ganzen werden zu Vierteln, und 17/5 wird über 17 : 5 = 3 Rest 2 zur gemischten Zahl. Mit Plus und Übertrag, Minus mit Entbündeln, Mal über unechte Brüche, zwei typischen Fallen 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 a mixed number means
A mixed number such as 2 3/4 consists of wholes and a fraction. Between them there is an invisible plus: 2 3/4 = 2 + 3/4. To turn it into a fraction, write the wholes as pieces with the same denominator: 2 = 2/1 = 8/4. Then count the pieces of equal size: 8/4 + 3/4 = 11/4. In short: wholes times denominator plus numerator, 2 · 4 + 3 = 11. Going back, the fraction bar means divided by: 17/5 = 17 : 5 = 3 remainder 2, so 3 2/5.
What the app shows
The calculation is shown as a large formula in the centre, and at each step the numbers glide to their new place. The invisible plus appears, the 2 becomes 2/1, arcs labelled “· 4” show the expansion to 8/4, and numerators merge into a sum. Below the formula one sentence explains each step. When adding, one whole is carried over to the wholes; when subtracting, one whole is split into pieces; and when multiplying, both numbers become fractions first.
Try it yourself
Choose the type of task: mixed number to fraction, fraction to mixed number, plus, minus or times. Set wholes, numerators and denominators with large buttons or ask for a new task. Two traps can be explored on purpose: reading 2 3/4 as 2 · 3/4 gives only 6/4, and multiplying “wholes by wholes, fraction by fraction” leads to a wrong result. In the Practice panel you choose the missing number yourself, when converting both ways and when carrying.
Frequently asked questions
- How do you convert a mixed number to a fraction?
- Multiply the wholes by the denominator, add the numerator and keep the denominator. Example: 2 3/4 = (2 · 4 + 3)/4 = 11/4, because 2 wholes are 8 quarters and 3 quarters are added.
- How do you convert an improper fraction to a mixed number?
- Divide the numerator by the denominator. The result is the number of wholes, the remainder becomes the numerator and the denominator stays: 17/5 = 17 : 5 = 3 remainder 2, so 3 2/5. Check: 3 · 5 + 2 = 17.
- How do you multiply mixed numbers?
- Convert both numbers to fractions first, then multiply: 1 1/2 · 2 1/3 = 3/2 · 7/3 = 7/2 = 3 1/2. Multiplying wholes by wholes and fraction by fraction would give the wrong 2 1/6, because the products 1 · 1/3 and 1/2 · 2 are missing.
- What can I try in the app?
- Converting mixed numbers to fractions and back, adding mixed numbers with carrying, subtracting by splitting a whole and multiplying, each step by step forwards and backwards. There are also two typical mistakes to compare and exercises with feedback on the formula.
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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