Evaluate each expression for p=-4, q=8, and r=-10. 3q/r - 5/p

Verified step by step guidance

1. Substitute the given values into the expression: \( \frac{3q}{r} - \frac{5}{p} \) becomes \( \frac{3(8)}{-10} - \frac{5}{-4} \).
2. Calculate \( 3 \times 8 \) to simplify the numerator of the first fraction.
3. Simplify the first fraction by dividing the result from step 2 by \(-10\).
4. Calculate \(-5\) divided by \(-4\) to simplify the second fraction.
5. Combine the results of the two fractions from steps 3 and 4 by subtracting the second fraction from the first.

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 to 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 involves division by p and r, which are both non-zero values. Understanding how to manipulate and simplify rational expressions is important for correctly evaluating the given expression without encountering undefined values.