Math worksheet on ratios using visual objects for elementary students.

Problem Analysis:

The worksheet involves solving ratio problems based on the images provided. Let's break it down step by step.

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Section 1: Butterflies and Houseflies

#### Image Description:
- There are 4 butterflies.
- There are 5 houseflies.

#### Questions:

##### a) What is the ratio of butterflies to houseflies?
- The ratio of butterflies to houseflies is calculated as:
$$
\text{Ratio} = \frac{\text{Number of butterflies}}{\text{Number of houseflies}} = \frac{4}{5}
$$
- Therefore, the ratio is 4:5.

##### b) The ratio of insects to butterflies is:
- Insects include both butterflies and houseflies. So, the total number of insects is:
$$
\text{Total insects} = \text{Butterflies} + \text{Houseflies} = 4 + 5 = 9
$$
- The ratio of insects to butterflies is:
$$
\text{Ratio} = \frac{\text{Total insects}}{\text{Butterflies}} = \frac{9}{4}
$$
- Therefore, the ratio is 9:4.

##### c) Write the ratio of houseflies to insects:
- The total number of insects is 9 (as calculated above).
- The ratio of houseflies to insects is:
$$
\text{Ratio} = \frac{\text{Houseflies}}{\text{Total insects}} = \frac{5}{9}
$$
- Therefore, the ratio is 5:9.

##### d) The ratio of houseflies to butterflies is:
- The ratio of houseflies to butterflies is:
$$
\text{Ratio} = \frac{\text{Houseflies}}{\text{Butterflies}} = \frac{5}{4}
$$
- Therefore, the ratio is 5:4.

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Section 2: Circles and Triangles

#### Image Description:
- There are 7 circles.
- There are 6 triangles.
- Total shapes = Circles + Triangles = 7 + 6 = 13.

#### Questions:

##### a) The ratio of circles to triangles is:
- The ratio of circles to triangles is:
$$
\text{Ratio} = \frac{\text{Circles}}{\text{Triangles}} = \frac{7}{6}
$$
- Therefore, the ratio is 7:6.

##### b) Write the ratio of triangles to circles:
- The ratio of triangles to circles is:
$$
\text{Ratio} = \frac{\text{Triangles}}{\text{Circles}} = \frac{6}{7}
$$
- Therefore, the ratio is 6:7.

##### c) The ratio of circles to shapes is:
- The total number of shapes is 13.
- The ratio of circles to shapes is:
$$
\text{Ratio} = \frac{\text{Circles}}{\text{Total shapes}} = \frac{7}{13}
$$
- Therefore, the ratio is 7:13.

##### d) What is the ratio of shapes to triangles?
- The total number of shapes is 13.
- The ratio of shapes to triangles is:
$$
\text{Ratio} = \frac{\text{Total shapes}}{\text{Triangles}} = \frac{13}{6}
$$
- Therefore, the ratio is 13:6.

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Final Answers:

1.
- a) 4:5
- b) 9:4
- c) 5:9
- d) 5:4

2.
- a) 7:6
- b) 6:7
- c) 7:13
- d) 13:6

Boxed Final Answer:

$$
\boxed{
\begin{array}{l}
\text{1. a) 4:5, b) 9:4, c) 5:9, d) 5:4} \\
\text{2. a) 7:6, b) 6:7, c) 7:13, d) 13:6}
\end{array}
}
$$