Let's analyze the information step by step and answer each part of the question:

To compare the numbers of squares, triangles, and circles, you can create a visual representation. For example:

Squares: 5 units

Triangles: 1 unit

Circles: 5 units (since the number of circles is 1/5 of the number of squares)

You can draw simple shapes or use numbers and ratios to represent this visually.

• Fraction of Circles to Triangles:

The fraction of the number of circles to the number of triangles is 1/5. This is because the number of circles is 1/5 of the number of triangles.

• Ratios of Shapes:

The ratio of the number of squares to the number of triangles to the number of circles is 5:1:5.

• Ratio of Triangles and Circles to Total Shapes:

To find the ratio of triangles and circles to the total number of shapes, you add the number of triangles and circles (1 + 5) and divide it by the total number of shapes (5 + 1 + 5).

So, the ratio is (1 + 5) : (5 + 1 + 5) = 6:11.

• Fraction of Circles to Total Shapes:

To express the number of circles as a fraction of the total number of shapes in its simplest form, you can use the ratio found in the previous step, which is 6:11. The fraction is 6/11.

So, in summary:

• Create a model to compare the numbers of squares, triangles, and circles.

• The fraction of the number of circles to the number of triangles is 1/5.

• The ratio of the number of squares to triangles to circles is 5:1:5.

• The ratio of triangles and circles to the total number of shapes is 6:11.

• The number of circles as a fraction of the total number of shapes in its simplest form is 6/11.

Verified answer

Answer:

1) To compare the numbers of squares, triangles, and circles, we can represent them using shapes. Let's use S for squares, T for triangles, and C for circles. Based on the given information, the model would look like this:

Squares: □ □ □ □ □

Triangles: △

Circles: ○

2) The fraction of the number of circles to the number of triangles can be calculated as follows:

Number of Circles / Number of Triangles

Since the number of circles is 1/5 of the number of squares, and the number of squares is 5 times the number of triangles, we can substitute these values into the fraction:

(1/5 * Number of Squares) / (1/5 * Number of Triangles)

This simplifies to:

Number of Squares / Number of Triangles

3) The ratio of the number of squares to the number of triangles to the number of circles can be expressed as:

Number of Squares : Number of Triangles : Number of Circles

Since the number of squares is 5 times the number of triangles, and the number of circles is 1/5 of the number of squares, the ratio becomes:

5 : 1 : (1/5 * Number of Squares)

Simplifying further:

5 : 1 : 1

4) To find the ratio of the number of triangles and circles to the total number of shapes, we need to add the number of triangles and circles together, and then divide them by the total number of shapes:

(Number of Triangles + Number of Circles) / (Number of Squares + Number of Triangles + Number of Circles)

Since the number of squares is 5 times the number of triangles, we can substitute this value:

(Number of Triangles + Number of Circles) / (5 * Number of Triangles + Number of Triangles + Number of Circles)

Simplifying further:

(Number of Triangles + Number of Circles) / (6 * Number of Triangles + Number of Circles)

5) To express the number of circles as a fraction of the total number of shapes in its simplest form, we divide the number of circles by the total number of shapes:

Number of Circles / (Number of Squares + Number of Triangles + Number of Circles)

Since the number of circles is 1/5 of the number of squares, and the number of squares is 5 times the number of triangles, we can substitute these values:

(1/5 * Number of Squares) / (Number of Squares + Number of Triangles + 1/5 * Number of Squares)

Simplifying further:

(1/5) / (1 + 1/5)

This fraction can be simplified to its simplest form, which is 1/6.