6th Grade Math Worksheet: Ratios with Geometric Shapes

Problem Analysis:

The worksheet asks for the ratios of different shapes in each question. Ratios compare the quantities of two or more items. The general format of a ratio is:

\[
\text{Ratio} = \frac{\text{Quantity of first item}}{\text{Quantity of second item}}
\]

We will solve each question step by step.

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Question 1: What is the ratio of triangles to circles?

#### Step 1: Count the triangles.
From the image, there are 2 triangles.

#### Step 2: Count the circles.
From the image, there are 3 circles.

#### Step 3: Write the ratio.
The ratio of triangles to circles is:

\[
\text{Ratio} = \frac{\text{Number of triangles}}{\text{Number of circles}} = \frac{2}{3}
\]

#### Final Answer for Question 1:
\[
\boxed{2:3}
\]

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Question 2: What is the ratio of stars to rectangles?

#### Step 1: Count the stars.
From the image, there are 5 stars.

#### Step 2: Count the rectangles.
From the image, there are 2 rectangles.

#### Step 3: Write the ratio.
The ratio of stars to rectangles is:

\[
\text{Ratio} = \frac{\text{Number of stars}}{\text{Number of rectangles}} = \frac{5}{2}
\]

#### Final Answer for Question 2:
\[
\boxed{5:2}
\]

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Question 3: What is the ratio of squares to circles?

#### Step 1: Count the squares.
From the image, there are 5 squares.

#### Step 2: Count the circles.
From the image, there are 3 circles.

#### Step 3: Write the ratio.
The ratio of squares to circles is:

\[
\text{Ratio} = \frac{\text{Number of squares}}{\text{Number of circles}} = \frac{5}{3}
\]

#### Final Answer for Question 3:
\[
\boxed{5:3}
\]

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Final Answers:

1. \(\boxed{2:3}\)
2. \(\boxed{5:2}\)
3. \(\boxed{5:3}\)

These are the solutions to the problems on the worksheet. Each ratio is expressed in the simplest form as requested.