Fraction Coloring Worksheets - Math Monks - Free Printable

Problem Overview:

The task involves comparing fractions and reducing them to their simplest forms. Once the fractions are reduced, they should be colored according to the provided color codes. The image shows a worksheet with various fractions in different sections of a cartoon character, and the goal is to simplify each fraction and apply the correct color based on the given key.

Color Codes:

- Red: $\frac{3}{5}$
- Green: $\frac{2}{5}$
- Brown: $\frac{4}{5}$
- Orange: $\frac{1}{6}$
- Violet: $\frac{4}{7}$
- Pink: $\frac{5}{6}$

Solution Approach:

1. Simplify Each Fraction: Reduce each fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD).
2. Match Simplified Fractions to Color Codes: Compare the simplified fractions to the given color codes and determine the appropriate color for each section.
3. Color the Worksheet: Use the matching colors to fill in the corresponding sections of the image.

Step-by-Step Simplification and Coloring:

#### 1. Simplify Each Fraction:
We will simplify each fraction listed in the image and match it to the color codes.

- $\frac{15}{25}$: GCD of 15 and 25 is 5. Simplify: $\frac{15 \div 5}{25 \div 5} = \frac{3}{5}$ → Red
- $\frac{6}{10}$: GCD of 6 and 10 is 2. Simplify: $\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$ → Red
- $\frac{11}{66}$: GCD of 11 and 66 is 11. Simplify: $\frac{11 \div 11}{66 \div 11} = \frac{1}{6}$ → Orange
- $\frac{9}{15}$: GCD of 9 and 15 is 3. Simplify: $\frac{9 \div 3}{15 \div 3} = \frac{3}{5}$ → Red
- $\frac{8}{20}$: GCD of 8 and 20 is 4. Simplify: $\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$ → Green
- $\frac{8}{48}$: GCD of 8 and 48 is 8. Simplify: $\frac{8 \div 8}{48 \div 8} = \frac{1}{6}$ → Orange
- $\frac{30}{50}$: GCD of 30 and 50 is 10. Simplify: $\frac{30 \div 10}{50 \div 10} = \frac{3}{5}$ → Red
- $\frac{3}{18}$: GCD of 3 and 18 is 3. Simplify: $\frac{3 \div 3}{18 \div 3} = \frac{1}{6}$ → Orange
- $\frac{6}{10}$: GCD of 6 and 10 is 2. Simplify: $\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$ → Red
- $\frac{10}{12}$: GCD of 10 and 12 is 2. Simplify: $\frac{10 \div 2}{12 \div 2} = \frac{5}{6}$ → Pink
- $\frac{20}{25}$: GCD of 20 and 25 is 5. Simplify: $\frac{20 \div 5}{25 \div 5} = \frac{4}{5}$ → Brown
- $\frac{33}{55}$: GCD of 33 and 55 is 11. Simplify: $\frac{33 \div 11}{55 \div 11} = \frac{3}{5}$ → Red
- $\frac{16}{20}$: GCD of 16 and 20 is 4. Simplify: $\frac{16 \div 4}{20 \div 4} = \frac{4}{5}$ → Brown
- $\frac{4}{10}$: GCD of 4 and 10 is 2. Simplify: $\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$ → Green
- $\frac{2}{12}$: GCD of 2 and 12 is 2. Simplify: $\frac{2 \div 2}{12 \div 2} = \frac{1}{6}$ → Orange
- $\frac{8}{14}$: GCD of 8 and 14 is 2. Simplify: $\frac{8 \div 2}{14 \div 2} = \frac{4}{7}$ → Violet
- $\frac{4}{24}$: GCD of 4 and 24 is 4. Simplify: $\frac{4 \div 4}{24 \div 4} = \frac{1}{6}$ → Orange
- $\frac{27}{45}$: GCD of 27 and 45 is 9. Simplify: $\frac{27 \div 9}{45 \div 9} = \frac{3}{5}$ → Red
- $\frac{20}{24}$: GCD of 20 and 24 is 4. Simplify: $\frac{20 \div 4}{24 \div 4} = \frac{5}{6}$ → Pink
- $\frac{9}{54}$: GCD of 9 and 54 is 9. Simplify: $\frac{9 \div 9}{54 \div 9} = \frac{1}{6}$ → Orange
- $\frac{28}{35}$: GCD of 28 and 35 is 7. Simplify: $\frac{28 \div 7}{35 \div 7} = \frac{4}{5}$ → Brown
- $\frac{5}{30}$: GCD of 5 and 30 is 5. Simplify: $\frac{5 \div 5}{30 \div 5} = \frac{1}{6}$ → Orange
- $\frac{12}{21}$: GCD of 12 and 21 is 3. Simplify: $\frac{12 \div 3}{21 \div 3} = \frac{4}{7}$ → Violet
- $\frac{8}{10}$: GCD of 8 and 10 is 2. Simplify: $\frac{8 \div 2}{10 \div 2} = \frac{4}{5}$ → Brown
- $\frac{15}{18}$: GCD of 15 and 18 is 3. Simplify: $\frac{15 \div 3}{18 \div 3} = \frac{5}{6}$ → Pink
- $\frac{12}{15}$: GCD of 12 and 15 is 3. Simplify: $\frac{12 \div 3}{15 \div 3} = \frac{4}{5}$ → Brown
- $\frac{16}{28}$: GCD of 16 and 28 is 4. Simplify: $\frac{16 \div 4}{28 \div 4} = \frac{4}{7}$ → Violet
- $\frac{6}{15}$: GCD of 6 and 15 is 3. Simplify: $\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$ → Green
- $\frac{10}{25}$: GCD of 10 and 25 is 5. Simplify: $\frac{10 \div 5}{25 \div 5} = \frac{2}{5}$ → Green
- $\frac{12}{30}$: GCD of 12 and 30 is 6. Simplify: $\frac{12 \div 6}{30 \div 6} = \frac{2}{5}$ → Green
- $\frac{7}{42}$: GCD of 7 and 42 is 7. Simplify: $\frac{7 \div 7}{42 \div 7} = \frac{1}{6}$ → Orange
- $\frac{10}{60}$: GCD of 10 and 60 is 10. Simplify: $\frac{10 \div 10}{60 \div 10} = \frac{1}{6}$ → Orange
- $\frac{32}{56}$: GCD of 32 and 56 is 8. Simplify: $\frac{32 \div 8}{56 \div 8} = \frac{4}{7}$ → Violet
- $\frac{21}{35}$: GCD of 21 and 35 is 7. Simplify: $\frac{21 \div 7}{35 \div 7} = \frac{3}{5}$ → Red
- $\frac{20}{35}$: GCD of 20 and 35 is 5. Simplify: $\frac{20 \div 5}{35 \div 5} = \frac{4}{7}$ → Violet

#### 2. Match Simplified Fractions to Colors:
Using the simplified fractions, we can now match them to the corresponding colors:
- Red: $\frac{3}{5}$
- Green: $\frac{2}{5}$
- Brown: $\frac{4}{5}$
- Orange: $\frac{1}{6}$
- Violet: $\frac{4}{7}$
- Pink: $\frac{5}{6}$

#### 3. Color the Worksheet:
Based on the matches, color each section of the image according to the simplified fractions.

Final Answer:

The final coloring of the worksheet would look like this (described in terms of colors):
- Red: All sections with $\frac{3}{5}$
- Green: All sections with $\frac{2}{5}$
- Brown: All sections with $\frac{4}{5}$
- Orange: All sections with $\frac{1}{6}$
- Violet: All sections with $\frac{4}{7}$
- Pink: All sections with $\frac{5}{6}$

The exact coloring would need to be applied manually to the image, but the process is clear.

$$
\boxed{\text{See the detailed steps above for the coloring guide.}}
$$