Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 5r/(2p - 3r)

Verified step by step guidance

1. Identify the given expression and the values of the variables: the expression is \(\frac{5r}{2p - 3r}\), with \(p = -4\), \(q = 8\), and \(r = -10\) (note that \(q\) is not used in this expression).
2. Substitute the given values of \(p\) and \(r\) into the expression: replace \(p\) with \(-4\) and \(r\) with \(-10\) in \(\frac{5r}{2p - 3r}\) to get \(\frac{5(-10)}{2(-4) - 3(-10)}\).
3. Simplify the numerator by multiplying \(5\) and \(-10\): calculate \(5 \times (-10)\).
4. Simplify the denominator by performing the operations inside it: calculate \(2 \times (-4)\) and \(-3 \times (-10)\), then subtract the second result from the first.
5. Write the simplified fraction with the results from the numerator and denominator, and then simplify the fraction if possible.

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This is essential for evaluating expressions like 5r / (2p - 3r) when specific values for p, q, and r are provided.

Order of Operations

The order of operations (PEMDAS/BODMAS) dictates the sequence in which parts of an expression are calculated. Correctly applying this ensures accurate evaluation, especially when dealing with fractions and multiple operations.

Simplifying Algebraic Expressions

Simplifying involves performing arithmetic operations and reducing expressions to their simplest form. This is crucial after substitution to combine terms and compute the final numerical value efficiently.