Operations with fractions involve addition, subtraction, multiplication, and division. Here are examples of each operation:

1. Addition of Fractions

To add fractions, they must have the same denominator.

Example: $\frac{2}{5} + \frac{3}{5} = \frac{2+3}{5} = \frac{5}{5} = 1$

If the denominators are different, find the least common denominator (LCD) and then add.

Example: $\frac{1}{4} + \frac{1}{6}$ The LCD of 4 and 6 is 12. $\frac{1 \times 3}{4 \times 3} + \frac{1 \times 2}{6 \times 2} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

2. Subtraction of Fractions

Subtraction is similar to addition; the fractions must have the same denominator.

Example: $\frac{7}{8} - \frac{3}{8} = \frac{7-3}{8} = \frac{4}{8} = \frac{1}{2}$

If the denominators are different, find the LCD and subtract.

Example: $\frac{5}{9} - \frac{1}{6}$ The LCD of 9 and 6 is 18. $\frac{5 \times 2}{9 \times 2} - \frac{1 \times 3}{6 \times 3} = \frac{10}{18} - \frac{3}{18} = \frac{7}{18}$

3. Multiplication of Fractions

Multiply the numerators together and the denominators together.

Example: $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$

4. Division of Fractions

To divide by a fraction, multiply by its reciprocal (invert the second fraction).

Example: $\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{3 \times 5}{4 \times 2} = \frac{15}{8}$

5. Simplifying Fractions

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example: $\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}$

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you find the least common denominator (LCD) of two fractions?
2. What are the steps to convert an improper fraction to a mixed number?
3. How do you convert a mixed number back into an improper fraction?
4. What is the process of comparing two fractions to determine which is larger?
5. How can you simplify a complex fraction?

Tip: When adding or subtracting fractions, always simplify the final answer if possible to make the fraction easier to understand or work with.