Evaluate each expression for p=-4, q=8, and r=-10. 5r / 2p-3r

Verified step by step guidance

1. Substitute the given values into the expression: replace \( r \) with \(-10\), \( p \) with \(-4\), and \( q \) with \(8\). The expression becomes \( \frac{5(-10)}{2(-4) - 3(-10)} \).
2. Calculate the numerator: \( 5 \times (-10) \).
3. Calculate the first part of the denominator: \( 2 \times (-4) \).
4. Calculate the second part of the denominator: \(-3 \times (-10) \).
5. Combine the results from the previous steps to simplify the expression: \( \frac{\text{numerator}}{\text{denominator}} \).

Key Concepts

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. In this question, we substitute p, q, and r with -4, 8, and -10, respectively, to evaluate the expression. This step is crucial for simplifying the expression to a numerical value.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating the expression, following this order is essential to arrive at the correct answer.

Rational Expressions

Rational expressions are fractions that contain polynomials in the numerator and denominator. In this case, the expression 5r / (2p - 3r) is a rational expression where we need to evaluate both the numerator and the denominator. Understanding how to simplify and evaluate these expressions is key to solving the problem accurately.