CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x —— • ——— 5 x²

Verified step by step guidance

1. Identify the given expression: \( \frac{2x}{5} \cdot \frac{10x}{x^2} \).
2. Multiply the numerators: \( 2x \times 10x = 20x^2 \).
3. Multiply the denominators: \( 5 \times x^2 = 5x^2 \).
4. Combine the results into a single fraction: \( \frac{20x^2}{5x^2} \).
5. Simplify the fraction by canceling common factors in the numerator and the denominator.

Key Concepts

Fraction Multiplication

To multiply fractions, you multiply the numerators together and the denominators together. In this case, you would multiply the expressions in the numerators (2x and 10x) and the expression in the denominator (5x²) to form a new fraction. Simplifying the resulting fraction is essential to express the answer in its lowest terms.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common factor (GCF). This process ensures that the fraction is expressed in the simplest form, making it easier to understand and work with. In this problem, identifying common factors in the resulting expression is crucial.

Algebraic Expressions

Algebraic expressions consist of numbers, variables, and operations. Understanding how to manipulate these expressions, including factoring and combining like terms, is vital for solving problems involving fractions. In this question, recognizing how to handle the variables and coefficients in the expressions will aid in performing the multiplication and simplification correctly.