Color by fraction activity for learning equivalent fractions with a fun lion theme.

Problem Overview:

The task involves coloring a picture based on the equivalence of fractions. The instructions provide specific colors for fractions that are equivalent to certain benchmark fractions (e.g., 1/2, 1/3, 1/4, etc.). The goal is to identify which fractions in the image are equivalent to these benchmarks and color them accordingly.

Key Steps to Solve:

1. Understand Fraction Equivalence: Two fractions are equivalent if they represent the same value. For example, \( \frac{3}{6} = \frac{1}{2} \) because both simplify to the same value.
2. Identify Benchmark Fractions: The problem specifies several benchmark fractions:
- Dark green: Equivalent to \( \frac{1}{2} \)
- Light green: Equivalent to \( \frac{1}{3} \)
- Blue: Equivalent to \( \frac{1}{4} \)
- Brown: Equivalent to \( \frac{1}{5} \)
- Orange: Equivalent to \( \frac{2}{5} \)
- Black: Equivalent to \( \frac{3}{5} \)
3. Simplify Each Fraction: Simplify each fraction in the image to its lowest terms to determine its equivalence to one of the benchmark fractions.
4. Color According to Instructions: Use the simplified fractions to determine the correct color for each section of the image.

Solution Process:

#### Step 1: Simplify Each Fraction
We will simplify each fraction in the image and check its equivalence to the benchmark fractions.

#### Fractions in the Image:
The image contains various fractions. Let's simplify them one by one:

- Top Row:
- \( \frac{1}{2} \): Already in simplest form.
- \( \frac{2}{4} \): Simplifies to \( \frac{1}{2} \).
- \( \frac{3}{6} \): Simplifies to \( \frac{1}{2} \).
- \( \frac{4}{8} \): Simplifies to \( \frac{1}{2} \).
- \( \frac{5}{10} \): Simplifies to \( \frac{1}{2} \).

- Second Row:
- \( \frac{1}{3} \): Already in simplest form.
- \( \frac{2}{6} \): Simplifies to \( \frac{1}{3} \).
- \( \frac{3}{9} \): Simplifies to \( \frac{1}{3} \).
- \( \frac{4}{12} \): Simplifies to \( \frac{1}{3} \).
- \( \frac{5}{15} \): Simplifies to \( \frac{1}{3} \).

- Third Row:
- \( \frac{1}{4} \): Already in simplest form.
- \( \frac{2}{8} \): Simplifies to \( \frac{1}{4} \).
- \( \frac{3}{12} \): Simplifies to \( \frac{1}{4} \).
- \( \frac{4}{16} \): Simplifies to \( \frac{1}{4} \).
- \( \frac{5}{20} \): Simplifies to \( \frac{1}{4} \).

- Fourth Row:
- \( \frac{1}{5} \): Already in simplest form.
- \( \frac{2}{10} \): Simplifies to \( \frac{1}{5} \).
- \( \frac{3}{15} \): Simplifies to \( \frac{1}{5} \).
- \( \frac{4}{20} \): Simplifies to \( \frac{1}{5} \).
- \( \frac{5}{25} \): Simplifies to \( \frac{1}{5} \).

- Fifth Row:
- \( \frac{2}{5} \): Already in simplest form.
- \( \frac{4}{10} \): Simplifies to \( \frac{2}{5} \).
- \( \frac{6}{15} \): Simplifies to \( \frac{2}{5} \).
- \( \frac{8}{20} \): Simplifies to \( \frac{2}{5} \).
- \( \frac{10}{25} \): Simplifies to \( \frac{2}{5} \).

- Sixth Row:
- \( \frac{3}{5} \): Already in simplest form.
- \( \frac{6}{10} \): Simplifies to \( \frac{3}{5} \).
- \( \frac{9}{15} \): Simplifies to \( \frac{3}{5} \).
- \( \frac{12}{20} \): Simplifies to \( \frac{3}{5} \).
- \( \frac{15}{25} \): Simplifies to \( \frac{3}{5} \).

#### Step 2: Color According to Instructions
Now, we color each section based on the simplified fractions:

- Dark Green (Equivalent to \( \frac{1}{2} \)):
- \( \frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10} \)

- Light Green (Equivalent to \( \frac{1}{3} \)):
- \( \frac{1}{3}, \frac{2}{6}, \frac{3}{9}, \frac{4}{12}, \frac{5}{15} \)

- Blue (Equivalent to \( \frac{1}{4} \)):
- \( \frac{1}{4}, \frac{2}{8}, \frac{3}{12}, \frac{4}{16}, \frac{5}{20} \)

- Brown (Equivalent to \( \frac{1}{5} \)):
- \( \frac{1}{5}, \frac{2}{10}, \frac{3}{15}, \frac{4}{20}, \frac{5}{25} \)

- Orange (Equivalent to \( \frac{2}{5} \)):
- \( \frac{2}{5}, \frac{4}{10}, \frac{6}{15}, \frac{8}{20}, \frac{10}{25} \)

- Black (Equivalent to \( \frac{3}{5} \)):
- \( \frac{3}{5}, \frac{6}{10}, \frac{9}{15}, \frac{12}{20}, \frac{15}{25} \)

Final Answer:

The final colored image should have sections colored as follows:
- Dark Green: All fractions equivalent to \( \frac{1}{2} \).
- Light Green: All fractions equivalent to \( \frac{1}{3} \).
- Blue: All fractions equivalent to \( \frac{1}{4} \).
- Brown: All fractions equivalent to \( \frac{1}{5} \).
- Orange: All fractions equivalent to \( \frac{2}{5} \).
- Black: All fractions equivalent to \( \frac{3}{5} \).

\[
\boxed{\text{See the detailed coloring based on the above instructions.}}
\]