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

Verified step by step guidance

1. Substitute the given values into the expression: \( \frac{q}{2} - \frac{r}{3} \div \frac{3p}{4} + \frac{q}{8} \) becomes \( \frac{8}{2} - \frac{-10}{3} \div \frac{3(-4)}{4} + \frac{8}{8} \).
2. Simplify each fraction: \( \frac{8}{2} = 4 \), \( \frac{-10}{3} \) remains as is, \( \frac{3(-4)}{4} = -3 \), and \( \frac{8}{8} = 1 \).
3. Rewrite the expression with simplified fractions: \( 4 - \frac{-10}{3} \div -3 + 1 \).
4. Address the division: \( \frac{-10}{3} \div -3 \) is equivalent to \( \frac{-10}{3} \times \frac{-1}{3} \).
5. Simplify the division result and then combine all terms: \( 4 + \text{result of division} + 1 \).

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 as it transforms the algebraic expression into a numerical one, allowing for straightforward calculations.

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. Applying these rules correctly is essential for accurately evaluating the expression given in the question.

Rational Expressions

Rational expressions are fractions that contain polynomials in the numerator and denominator. In this question, the expression involves division of two rational expressions, which requires careful handling of the numerator and denominator. Understanding how to simplify and evaluate these expressions is key to finding the correct answer.