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Multiplying fractions is a fundamental operation in mathematics, particularly in arithmetic and algebra. When multiplying fractions, we follow specific rules to simplify the process and obtain the result.

Basic Concepts

To multiply fractions, it's important to understand the following concepts:

• Fractions: Numbers that represent parts of a whole or ratios of two quantities.
• Multiplying fractions: The process of finding the product of two or more fractions.

Multiplication Techniques

There are several techniques to multiply fractions:

• Straight multiplication: Multiply the numerators together and the denominators together to get the product.
• Cancellation: Cancel common factors between numerators and denominators before multiplying.

Examples

Let's consider a few examples to illustrate the multiplication of fractions:

Example 1:

Multiply $$\frac{2}{3}$$ by $$\frac{4}{5}$$

Using straight multiplication, we multiply the numerators together and the denominators together:

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

Example 2:

Multiply $$\frac{3}{7}$$ by $$\frac{5}{9}$$

Using cancellation, we cancel common factors between numerators and denominators:

$$\frac{3}{7}\times \frac{5}{9}=\frac{3\times 5}{7\times 9}=\frac{15}{63}$$

After simplification, we get the result as $$\frac{5}{21}$$.

Conclusion

Multiplying fractions is a fundamental operation that finds applications in various mathematical contexts. Mastering the techniques of fraction multiplication enables efficient problem-solving and enhances mathematical understanding.