Final answer:
An area model for 1/2 multiplied by 2/3 is a rectangle divided into six equal parts, with two parts colored to represent the product which is 1/3.
Step-by-step explanation:
To create an area model for 1/2 multiplied by 2/3, we can visualize the multiplication of fractions as the area of a rectangle. Start with a rectangle and divide it into two equal parts to represent the fraction 1/2. Color in one of the two parts. Now, take that colored half and further divide it into three equal parts to represent the fraction 2/3. Color in two of these three parts within the already colored half.
The overlapping colored area in both the division by halves and thirds represents the fraction 1/2 × 2/3. In total, out of the six sections of the original rectangle, 2 are colored, which gives us 2/6 or 1/3 as the product. So, the area model has one-third of the original rectangle colored in to show the product of these two fractions.