Students solve fraction multiplication problems to reveal a mystery picture by coloring squares according to the key.

Problem Overview:

The task involves solving a series of fraction multiplication problems and then coloring the corresponding cells in a grid based on the answers. The goal is to reveal a "mystery picture" by correctly solving the problems and applying the color codes provided.

Step-by-Step Solution:

#### 1. Solve Each Fraction Multiplication Problem:

We will solve each problem step by step:

1. Problem 1: \( \frac{2}{7} \times \frac{1}{8} \)
\[
\frac{2}{7} \times \frac{1}{8} = \frac{2 \times 1}{7 \times 8} = \frac{2}{56} = \frac{1}{28}
\]
- Answer: \( \frac{1}{28} \)
- Color: Orange

2. Problem 2: \( \frac{3}{5} \times \frac{1}{5} \)
\[
\frac{3}{5} \times \frac{1}{5} = \frac{3 \times 1}{5 \times 5} = \frac{3}{25}
\]
- Answer: \( \frac{3}{25} \)
- Color: Black

3. Problem 3: \( \frac{1}{6} \times \frac{1}{5} \)
\[
\frac{1}{6} \times \frac{1}{5} = \frac{1 \times 1}{6 \times 5} = \frac{1}{30}
\]
- Answer: \( \frac{1}{30} \)
- Color: Yellow

4. Problem 4: \( \frac{1}{3} \times \frac{1}{7} \)
\[
\frac{1}{3} \times \frac{1}{7} = \frac{1 \times 1}{3 \times 7} = \frac{1}{21}
\]
- Answer: \( \frac{1}{21} \)
- Color: Light Blue

5. Problem 5: \( \frac{9}{8} \times \frac{5}{9} \)
\[
\frac{9}{8} \times \frac{5}{9} = \frac{9 \times 5}{8 \times 9} = \frac{45}{72} = \frac{5}{8}
\]
- Answer: \( \frac{5}{8} \)
- Color: Brown

6. Problem 6: \( \frac{3}{5} \times \frac{2}{5} \)
\[
\frac{3}{5} \times \frac{2}{5} = \frac{3 \times 2}{5 \times 5} = \frac{6}{25}
\]
- Answer: \( \frac{6}{25} \)
- Color: White

7. Problem 7: \( \frac{4}{9} \times \frac{4}{7} \)
\[
\frac{4}{9} \times \frac{4}{7} = \frac{4 \times 4}{9 \times 7} = \frac{16}{63}
\]
- Answer: \( \frac{16}{63} \)
- Color: Red

8. Problem 8: \( \frac{1}{5} \times \frac{6}{4} \)
\[
\frac{1}{5} \times \frac{6}{4} = \frac{1 \times 6}{5 \times 4} = \frac{6}{20} = \frac{3}{10}
\]
- Answer: \( \frac{3}{10} \)
- Color: Orange

9. Problem 9: \( \frac{10}{3} \times \frac{4}{5} \)
\[
\frac{10}{3} \times \frac{4}{5} = \frac{10 \times 4}{3 \times 5} = \frac{40}{15} = \frac{8}{3}
\]
- Answer: \( \frac{8}{3} \)
- Color: Black

10. Problem 10: \( \frac{2}{12} \times \frac{1}{9} \)
\[
\frac{2}{12} \times \frac{1}{9} = \frac{2 \times 1}{12 \times 9} = \frac{2}{108} = \frac{1}{54}
\]
- Answer: \( \frac{1}{54} \)
- Color: Yellow

#### 2. Apply the Colors to the Grid:

Using the answers and their corresponding colors, we would shade the cells in the grid as follows (assuming the grid coordinates are provided in the image):

- Orange: Cells corresponding to \( \frac{1}{28} \) and \( \frac{3}{10} \)
- Black: Cells corresponding to \( \frac{3}{25} \) and \( \frac{8}{3} \)
- Yellow: Cells corresponding to \( \frac{1}{30} \) and \( \frac{1}{54} \)
- Light Blue: Cells corresponding to \( \frac{1}{21} \)
- Brown: Cells corresponding to \( \frac{5}{8} \)
- White: Cells corresponding to \( \frac{6}{25} \)
- Red: Cells corresponding to \( \frac{16}{63} \)

#### 3. Reveal the Mystery Picture:

After shading all the cells according to the solutions and color codes, the mystery picture should emerge. This is typically a simple geometric shape or design.

Final Answer:

\[
\boxed{\text{Solve each problem, apply the colors, and reveal the mystery picture.}}
\]

If you provide the grid coordinates for each answer, I can help shade the specific cells!