Multiply fractions by whole numbers using models – identify the correct visual representation for each multiplication problem.

Problem Description:

The task involves multiplying fractions by whole numbers using visual models. The goal is to choose the correct model that represents the product of the given fraction and whole number.

Given Problems:

1. Part (a): \( \frac{2}{6} \times 3 \)
2. Part (b): \( \frac{3}{5} \times 3 \)
3. Part (c): \( \frac{9}{10} \times 2 \)

Solution:

#### Part (a): \( \frac{2}{6} \times 3 \)

1. Understanding the Problem:
- The fraction \( \frac{2}{6} \) means 2 parts out of 6.
- Multiplying by 3 means taking 3 groups of \( \frac{2}{6} \).

2. Calculation:
\[
\frac{2}{6} \times 3 = \frac{2 \times 3}{6} = \frac{6}{6} = 1
\]
- This means the entire grid should be shaded.

3. Visual Model:
- The correct model should show a fully shaded grid (since \( \frac{6}{6} = 1 \)).

4. Choice:
- The correct model is the one where all squares are shaded.

#### Part (b): \( \frac{3}{5} \times 3 \)

1. Understanding the Problem:
- The fraction \( \frac{3}{5} \) means 3 parts out of 5.
- Multiplying by 3 means taking 3 groups of \( \frac{3}{5} \).

2. Calculation:
\[
\frac{3}{5} \times 3 = \frac{3 \times 3}{5} = \frac{9}{5}
\]
- Since \( \frac{9}{5} \) is an improper fraction, it can be converted to a mixed number:
\[
\frac{9}{5} = 1 \frac{4}{5}
\]
- This means 1 whole grid plus 4 out of 5 parts in another grid.

3. Visual Model:
- The correct model should show one fully shaded grid and 4 out of 5 parts shaded in another grid.

4. Choice:
- The correct model is the one with one fully shaded grid and 4 out of 5 parts shaded in another grid.

#### Part (c): \( \frac{9}{10} \times 2 \)

1. Understanding the Problem:
- The fraction \( \frac{9}{10} \) means 9 parts out of 10.
- Multiplying by 2 means taking 2 groups of \( \frac{9}{10} \).

2. Calculation:
\[
\frac{9}{10} \times 2 = \frac{9 \times 2}{10} = \frac{18}{10}
\]
- Since \( \frac{18}{10} \) is an improper fraction, it can be converted to a mixed number:
\[
\frac{18}{10} = 1 \frac{8}{10} = 1 \frac{4}{5}
\]
- This means 1 whole grid plus 4 out of 5 parts in another grid.

3. Visual Model:
- The correct model should show one fully shaded grid and 4 out of 5 parts shaded in another grid.

4. Choice:
- The correct model is the one with one fully shaded grid and 4 out of 5 parts shaded in another grid.

Final Answers:

- Part (a): The model where all squares are shaded.
- Part (b): The model with one fully shaded grid and 4 out of 5 parts shaded in another grid.
- Part (c): The model with one fully shaded grid and 4 out of 5 parts shaded in another grid.

\[
\boxed{\text{See explanations above for detailed reasoning.}}
\]