Vibrant educational guide showing how to add, subtract, multiply, and divide fractions with clear examples and instructions.

The image you've uploaded is an educational poster titled "Operations with Fractions", which explains how to perform four basic operations—addition, subtraction, multiplication, and division—with fractions. Let's go through each section step by step and explain the rules and examples provided.

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🔹 1. Addition of Fractions

Example:
$$
\frac{1}{4} + \frac{3}{8}
$$

#### Steps:
- Step 1: If denominators are different, find a common denominator.
- The least common denominator (LCD) of 4 and 8 is 8.
- Convert $\frac{1}{4}$ to an equivalent fraction with denominator 8:
$$
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
$$
- Step 2: Add the numerators (denominators stay the same):
$$
\frac{2}{8} + \frac{3}{8} = \frac{5}{8}
$$

✔ Final Answer: $\boxed{\frac{5}{8}}$

> ✔ Rule: Always find a common denominator before adding or subtracting fractions.

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🔹 2. Subtraction of Fractions

Example:
$$
\frac{5}{6} - \frac{3}{4}
$$

#### Steps:
- Step 1: Find a common denominator.
- LCD of 6 and 4 is 12.
- Convert both fractions:
$$
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}, \quad
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$
- Step 2: Subtract the numerators:
$$
\frac{10}{12} - \frac{9}{12} = \frac{1}{12}
$$

✔ Final Answer: $\boxed{\frac{1}{12}}$

> ✔ Rule: Same as addition — use common denominator, then subtract numerators.

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🔹 3. Multiplication of Fractions

Example:
$$
\frac{3}{4} \times \frac{4}{5}
$$

#### Steps:
- Multiply the numerators: $3 \times 4 = 12$
- Multiply the denominators: $4 \times 5 = 20$
- Result: $\frac{12}{20}$
- Reduce the fraction:
$$
\frac{12}{20} = \frac{3}{5} \quad \text{(divided numerator and denominator by 4)}
$$

✔ Final Answer: $\boxed{\frac{3}{5}}$

> ✔ Rule: Multiply numerators together, multiply denominators together, then simplify.

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🔹 4. Division of Fractions

Example:
$$
\frac{4}{5} \div \frac{5}{6}
$$

#### Steps:
- Step 1: Invert the divisor (second fraction):
$$
\frac{5}{6} \rightarrow \frac{6}{5}
$$
- Step 2: Change division to multiplication:
$$
\frac{4}{5} \div \frac{5}{6} = \frac{4}{5} \times \frac{6}{5}
$$
- Multiply:
- Numerators: $4 \times 6 = 24$
- Denominators: $5 \times 5 = 25$
- Result: $\frac{24}{25}$

✔ Final Answer: $\boxed{\frac{24}{25}}$

> ✔ Rule: "Keep, Change, Flip" — keep the first fraction, change division to multiplication, flip the second fraction.

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🟨 Important Reminder at Bottom:

> "Remember to Reduce!"
> For all operations, always simplify (reduce) the final answer if possible.

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✔ Summary of Key Rules:

| Operation | Rule |
|---------|------|
| Addition/Subtraction | Find common denominator → add/subtract numerators |
| Multiplication | Multiply numerators × numerators, denominators × denominators → reduce |
| Division | Keep first, change to ×, flip second (invert divisor) → multiply |

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This poster is a great visual guide for learning and remembering how to work with fractions. It emphasizes clarity and simplicity in each operation, making it ideal for students.

Let me know if you'd like practice problems or help solving a specific fraction problem!