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The following is an example with the discrete model.

To solve the problem of representing the various shapes in the diagram as fractions of the total number of shapes, we can follow these steps:

1. **Count the Total Number of Shapes:**
   First, we need to count the total number of shapes in the grid.

2. **Identify the Number of Each Shape:**
   Then, we'll count how many of each specific shape (circles, squares, and triangles) are present.

3. **Calculate the Fractions:**
   For each shape, we'll represent its count as a fraction of the total number of shapes.

### Step 1: Count the Total Number of Shapes
The grid consists of 5 rows and 9 columns, so there are \( 5 \times 9 = 45 \) shapes in total.

### Step 2: Identify the Number of Each Shape
- **Circles:** The total number of circles in the grid.
- **Squares:** The total number of squares in the grid.
- **Triangles:** The total number of triangles in the grid.

### Step 3: Calculate the Fractions
Let’s count each shape:

- **Circles:** There are 14 circles (7 on each side).
- **Squares:** There are 25 squares (including the 9 that frame the triangles).
- **Triangles:** There are 6 triangles.

Now, the fractions for each shape:
- **Fraction of Circles:** \(\frac{14}{45}\)
- **Fraction of Squares:** \(\frac{25}{45}\), which simplifies to \(\frac{5}{9}\).
- **Fraction of Triangles:** \(\frac{6}{45}\), which simplifies to \(\frac{2}{15}\).

### Summary
- **Fraction of Circles:** \(\frac{14}{45}\)
- **Fraction of Squares:** \(\frac{5}{9}\)
- **Fraction of Triangles:** \(\frac{2}{15}\)

Would you like further details on any part of this solution, or do you have any additional questions?

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**Related Questions:**

1. How do you simplify fractions?
2. What is the process of converting a fraction to a decimal?
3. How do you determine the proportion of different shapes in a different grid?
4. How would you calculate the percentage of each shape in this grid?
5. What other ways could you represent the distribution of shapes (e.g., ratio, percentage)?

**Tip:** When working with fractions, always check if you can simplify them to their lowest terms for a clearer representation.

Using the diagram below, represent each of the following as a fraction of all shapes shown.

Learn how to calculate the fraction of each shape in a grid diagram. This problem involves counting different shapes and representing them as fractions of the total number of shapes. Suitable for students in Grades 4-6.

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