Question

2 which model represents $4 \times \frac{2}{3}$?
f
two circles divided into three parts, two shaded in each
g
four circles divided into five parts, two shaded in each
h
four circles divided into three parts, two shaded in each
j
two circles divided into five parts, two shaded in each

Explanation:

Step1: Analyze the meaning of \(4\times\frac{2}{3}\)

\(4\times\frac{2}{3}\) means adding \(\frac{2}{3}\) four times.

Step2: Analyze each option

• Option F: Each circle is divided into 3 - equal parts. Each circle has 2 shaded parts (representing \(\frac{2}{3}\)), but there are only 2 circles. The total shaded parts represent \(2\times\frac{2}{3}\), not \(4\times\frac{2}{3}\).
• Option G: Each circle is divided into 5 - equal parts. The fraction represented is \(\frac{2}{5}\) per circle. The total shaded parts represent \(4\times\frac{2}{5}\), not \(4\times\frac{2}{3}\).
• Option H: Each circle is divided into 3 - equal parts. Each circle has 2 shaded parts (representing \(\frac{2}{3}\)). There are 4 circles. The total shaded parts represent \(4\times\frac{2}{3}\).
• Option J: Each circle is divided into 5 - equal parts. The fraction represented is \(\frac{3}{5}\) per circle. The total shaded parts represent \(2\times\frac{3}{5}\), not \(4\times\frac{2}{3}\).

Answer:

H.