Does expanding make a fraction bigger?

No. Numerator and denominator get bigger, but the pieces get smaller. 2/3 and 8/12 describe exactly the same share; on the bar the coloured area is the same.

When can you simplify a fraction?

When numerator and denominator have a common factor greater than 1. 6/8 can be simplified by 2 (3/4), but not by 3, because 3 divides 6 but not 8. Simplifying by the greatest common factor gives the fully simplified fraction.

Can you add the same number on top and bottom?

No, that changes the share. With “+1 on top and bottom” 2/3 becomes 3/4, and 3/4 is more than 2/3. You may not cancel terms of a sum either: (2+3)/(2+5) is 5/7, not 3/5.

What can I try in the app?

Expand and simplify fractions on a chocolate bar, let the chain of equal fractions grow, see failed attempts at simplifying, test the wrong trick with a comparison bar and solve practice tasks with feedback on the bar.

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Erweitern und Kürzen

About this app

Eine Schokoladentafel wird feiner geschnitten oder Stücke werden zusammengefasst: Zähler und Nenner ändern sich, die gefärbte Fläche bleibt gleich. Mit Bruchkette, Kürzen nur mit gemeinsamem Teiler, dem Falsch-Trick „+1 oben und unten“ und Übungsaufgaben.

With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.

What expanding and simplifying mean

Expanding a fraction means multiplying numerator and denominator by the same number: 2/3 = 4/6 = 8/12. Simplifying means dividing numerator and denominator by the same number. This only works with a common factor, and a fraction is fully simplified when numerator and denominator share only the factor 1. Both steps change only how the fraction is written: it still describes the same share. You need them to compare fractions, to find a common denominator and to give results in their simplest form. In the Baden-Württemberg curriculum the topic belongs to years 5 and 6.

What the app shows

A chocolate bar with a fixed coloured area. When expanding, a knife sweeps across every piece: 3 pieces become 6, 2 coloured pieces become 4, and the bracket above the share stays put. When simplifying, frames appear around every k pieces and the inner lines disappear. If k does not fit, dashed groups stick out over the bar. Below, a chain of small bars grows. The wrong trick “+1 on top and bottom” puts a comparison bar below: 2/3 becomes 3/4, and the hatched strip shows that this is more chocolate.

Try it yourself

Choose a starting fraction or tap a piece of the bar. Drag the handle next to the bar downwards to cut finer, or simplify by 2, 3, 4, 5 or 6 and see when the groups fit. The Practice panel has short tasks: expand, simplify, fully simplify, fill in a missing number, recognise equivalent fractions and decide whether you may cancel in a sum. Every answer shows the correct transformation on the bar, and a wrong answer appears as a comparison bar.

Frequently asked questions

Does expanding make a fraction bigger?: No. Numerator and denominator get bigger, but the pieces get smaller. 2/3 and 8/12 describe exactly the same share; on the bar the coloured area is the same.
When can you simplify a fraction?: When numerator and denominator have a common factor greater than 1. 6/8 can be simplified by 2 (3/4), but not by 3, because 3 divides 6 but not 8. Simplifying by the greatest common factor gives the fully simplified fraction.
Can you add the same number on top and bottom?: No, that changes the share. With “+1 on top and bottom” 2/3 becomes 3/4, and 3/4 is more than 2/3. You may not cancel terms of a sum either: (2+3)/(2+5) is 5/7, not 3/5.
What can I try in the app?: Expand and simplify fractions on a chocolate bar, let the chain of equal fractions grow, see failed attempts at simplifying, test the wrong trick with a comparison bar and solve practice tasks with feedback on the bar.

Subject: Bruchrechnung (Klasse 6)

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