Question

in the models, each circle represents one whole. which model represents the multiplication problem \\(\frac{2}{6} \times 3\\)?

Explanation:

Interpret the multiplication expression

$$ \frac{2}{6} \times 3 $$

This represents having \(3\) groups, where each group contains a fraction of \(\frac{2}{6}\).

Analyze the visual models

• Each circle represents one whole, divided into \(6\) equal sectors.
• A fraction of \(\frac{2}{6}\) is represented by shading exactly \(2\) out of the \(6\) sectors in a circle.
• Multiplying by \(3\) means we need \(3\) such circles, each having exactly \(2\) sectors shaded.

Match with the options

• Option 1: Three circles, each with \(4\) sectors shaded (\(\frac{4}{6} \times 3\)).
• Option 2: Two circles, each with \(2\) sectors shaded (\(\frac{2}{6} \times 2\)).
• Option 3: Three circles, each with \(2\) sectors shaded (\(\frac{2}{6} \times 3\)).
• Option 4: Three circles, each with \(1\) sector shaded (\(\frac{1}{6} \times 3\)).

Answer:

• (A) Three circles, each with 4 sectors shaded
• (B) Two circles, each with 2 sectors shaded
• (C) Three circles, each with 2 sectors shaded (Correct answer)
• (D) Three circles, each with 1 sector shaded