Evaluate each expression for p=-4, q=8, and r=-10. 3q/r - 5/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: \( \frac{3q}{r} - \frac{5}{p} \).
3. Substitute the given values into the expression: \( \frac{3 \times 8}{-10} - \frac{5}{-4} \).
4. Simplify each fraction separately: calculate \( \frac{24}{-10} \) and \( \frac{5}{-4} \).
5. Combine the simplified fractions by performing the subtraction: \( \frac{24}{-10} - \left(-\frac{5}{4}\right) \).

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This is essential for evaluating expressions when specific values for variables are provided, allowing the expression to be simplified to a numerical result.

Order of Operations

The order of operations dictates the sequence in which parts of a mathematical expression are evaluated, typically following PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Correct application ensures accurate simplification of expressions.

Operations with Negative Numbers

Understanding how to handle negative numbers in arithmetic operations like division and subtraction is crucial. This includes knowing that dividing by a negative number changes the sign of the result and that subtracting a negative is equivalent to addition.