Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. (q + r)/ (q + p)

Verified step by step guidance

1. Identify the given values: \(p = -4\), \(q = 8\), and \(r = -10\).
2. Rewrite the expression clearly. The problem states: \(q + r \quad q + p\). This likely means two separate expressions: \(q + r\) and \(q + p\).
3. Substitute the given values into the first expression: replace \(q\) with 8 and \(r\) with -10 in \(q + r\), so it becomes \$8 + (-10)$.
4. Substitute the given values into the second expression: replace \(q\) with 8 and \(p\) with -4 in \(q + p\), so it becomes \$8 + (-4)$.
5. Simplify each expression by performing the addition to find the numerical results for both \(q + r\) and \(q + p\).

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This is essential for evaluating expressions like q + r or q + p by directly inserting the values of p, q, and r into the expression.

Order of Operations

The order of operations dictates the sequence in which parts of a mathematical expression are evaluated. Understanding this ensures correct evaluation of expressions, especially when multiple operations like addition and multiplication are involved.

Basic Arithmetic Operations

Basic arithmetic operations such as addition and multiplication are fundamental for simplifying expressions. Knowing how to correctly perform these operations with positive and negative numbers is crucial for accurate evaluation.