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

Verified step by step guidance

1. Identify the expression to evaluate: \( \frac{q + r}{q + p} \).
2. Substitute the given values into the expression: \( q = 8 \), \( r = -10 \), and \( p = -4 \).
3. Replace \( q \), \( r \), and \( p \) in the expression: \( \frac{8 + (-10)}{8 + (-4)} \).
4. Simplify the numerator: \( 8 + (-10) \).
5. Simplify the denominator: \( 8 + (-4) \).

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 and obtaining a numerical result.

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 q + r / q + p involves both addition and division of values. Understanding how to manipulate and simplify rational expressions is key to solving problems involving them, especially when substituting values.