Question

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which model represents the product $5\times\frac{9}{12}$?

Explanation:

Step1: Calculate the product

$$5\times\frac{9}{12}=\frac{5\times9}{12}=\frac{45}{12}=\frac{15}{4}=3\frac{3}{4}$$
This means we need to find a model that represents \(3\frac{3}{4}\). Each whole circle is divided into 12 equal - parts. \(3\frac{3}{4}=\frac{15}{4}=\frac{45}{12}\).

Step2: Analyze the first set of models

The first set has 2 circles. One circle is almost full (but not 3 full circles) and the other has a small portion shaded. This does not represent \(3\frac{3}{4}\).

Step3: Analyze the second set of models

The second set has 4 circles. Three of them are completely shaded (representing 3 wholes). The fourth circle: \(\frac{3}{4}=\frac{9}{12}\) (since if a circle is divided into 12 parts, \(\frac{3}{4}\times12 = 9\) parts are shaded).

Answer:

The second set of models (the one with four circles, three fully shaded and the fourth with 9 out of 12 parts shaded) represents \(5\times\frac{9}{12}\).