How do you multiply two fractions?

Numerator times numerator and denominator times denominator, then simplify. Example: 2/3 · 3/4 = 6/12 = 1/2. You do not need a common denominator to multiply.

Why is 4 · 1/7 not 4/28?

4 · 1/7 means four times one seventh, which is 4/7. The pieces stay sevenths, only their number grows. 4/28 simplifies to 1/7, so it is only as big as a single piece.

Does multiplying always make a number bigger?

No. If one factor is smaller than 1, the result is smaller than the other factor: half of three quarters, 3/8, is less than 3/4. Only factors bigger than 1 make it bigger.

What can I try in the app?

A number times a fraction, a fraction times a fraction in the area model, and the size comparison with a factor scale, each step by step. There are also random tasks with feedback in the scene.

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Brüche multiplizieren: Anteil vom Anteil

About this app

Die Hälfte von drei Vierteln an der Schokoladentafel: Im Flächenmodell überlappen sich die Streifen, Zahl mal Bruch wird zum wiederholten Addieren auf dem Zahlenstrahl, und der Größenvergleich zeigt, warum ein Faktor kleiner als 1 kleiner macht. Mit Schrittanimation und Übungsaufgaben.

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

How to multiply fractions

A fraction times a fraction means a part of a part: 1/2 · 3/4 is half of three quarters. You multiply numerator by numerator and denominator by denominator, so (1 · 3)/(2 · 4) = 3/8, and simplify at the end. You do not need a common denominator; that is only needed for adding and subtracting. A whole number times a fraction is repeated addition: 4 · 1/7 = 1/7 + 1/7 + 1/7 + 1/7 = 4/7. Only the numerator is multiplied, the denominator stays the same.

What the app shows

In the area model a bar of chocolate is the whole. Step by step, three quarters are coloured across, the bar is cut into columns and half of the coloured part is taken; the overlap is the result, 3 of 8 pieces. For a number times a fraction, the pieces jump end to end along the number line, and the typical mistake 4/28 appears as its own strip: it is only as big as a single seventh. A third mode compares the result with the second factor on a factor scale around 1.

Try it yourself

Set numerators and denominators with large buttons or drag directly on the bar, and play the steps one by one or all at once. Try a first factor smaller than 1, exactly 1 and bigger than 1 and see whether the result shrinks, stays the same or grows. The Practise panel gives you random tasks with fraction input; the feedback shows in the scene why an answer is right and spots mistakes such as multiplying the denominator as well or using an unnecessary common denominator.

Frequently asked questions

How do you multiply two fractions?: Numerator times numerator and denominator times denominator, then simplify. Example: 2/3 · 3/4 = 6/12 = 1/2. You do not need a common denominator to multiply.
Why is 4 · 1/7 not 4/28?: 4 · 1/7 means four times one seventh, which is 4/7. The pieces stay sevenths, only their number grows. 4/28 simplifies to 1/7, so it is only as big as a single piece.
Does multiplying always make a number bigger?: No. If one factor is smaller than 1, the result is smaller than the other factor: half of three quarters, 3/8, is less than 3/4. Only factors bigger than 1 make it bigger.
What can I try in the app?: A number times a fraction, a fraction times a fraction in the area model, and the size comparison with a factor scale, each step by step. There are also random tasks with feedback in the scene.

Subject: Bruchrechnung (Klasse 6)

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