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

Verified step by step guidance

1. Identify the given values: \( p = -4 \), \( q = 8 \), and \( r = -10 \).
2. Write down the expression to evaluate: \( \frac{q + r}{q + p} \).
3. Substitute the given values into the expression: \( \frac{8 + (-10)}{8 + (-4)} \).
4. Simplify the numerator and denominator separately: numerator is \( 8 - 10 \), denominator is \( 8 - 4 \).
5. Write the simplified fraction \( \frac{8 - 10}{8 - 4} \) and prepare to simplify further.

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This step is essential to evaluate the expression for specific values of p, q, and r, allowing you to simplify and calculate the result.

Order of Operations

The order of operations (PEMDAS) dictates the sequence in which parts of an expression are evaluated: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Correct application ensures accurate evaluation of expressions.

Simplifying Rational Expressions

A rational expression is a fraction where the numerator and denominator are expressions. Simplifying involves performing arithmetic operations on both parts and reducing the fraction if possible, which is necessary to find the final value of the given expression.