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Chapter 11: Problem 5

Evaluate. \(\frac{3 p}{q},\) when \(p=-2\) and \(q=6\)

Short Answer

Expert verified
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Step by step solution

01

Identify Values

Start by identifying the given values. We have \(p = -2\) and \(q = 6\).
02

Substitute Values into the Expression

Substitute \(p\) and \(q\) into the expression \(\frac{3p}{q}\). So the expression becomes \(\frac{3(-2)}{6}\).
03

Multiply the Numerator

Multiply the constants in the numerator: \(3 \times (-2) = -6\). This modifies the expression to \(\frac{-6}{6}\).
04

Simplify the Fraction

Simplify the fraction \(\frac{-6}{6}\). This is equal to \(-1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Evaluating Expressions
Evaluating expressions is a crucial part of basic algebra. It involves finding the value of an expression by replacing the variables with given numbers. Let's break it down with an example. Imagine you have the expression \(\frac{3p}{q}\).
To evaluate this:
  • First, identify the values you need to substitute. Here, it's given that \(p = -2\) and \(q = 6\).
  • Replace the variables in the expression with these values. So, \(\frac{3p}{q}\) becomes \(\frac{3(-2)}{6}\).
  • Then, follow the rules of arithmetic to simplify.
By working step-by-step, you can easily find the value of the expression.
Substitution
Substitution involves replacing variables in an expression with their given values. It is one of the foundational techniques in algebra. Using the example \(\frac{3p}{q}\), we can see how simple substitution can be.
  • Firstly, identify the given values for the variables in your expression. Here, \(p = -2\) and \(q = 6\).
  • Next, substitute those values into the expression. This changes your expression from \(\frac{3p}{q}\) to \(\frac{3(-2)}{6}\).
  • After substitution, you proceed with arithmetic operations to simplify the expression. Remember, you must follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Substitution helps us take abstract expressions and turn them into simple arithmetic.
Simplifying Fractions
Simplifying fractions is the process of breaking down a fraction to its simplest form. Let鈥檚 use our previous example \(\frac{3(-2)}{6}\):
  • After substituting and multiplying, you might get a fraction like \(\frac{-6}{6}\). This involves simplifying the fraction.
  • To do this, divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, both -6 and 6 can be divided by 6.
  • So, \(\frac{-6 \div 6}{6 \div 6} = \frac{-1}{1} = -1\).
Simplifying helps in making fractions easier to understand and work with. It ensures that the answers are always presented in the most straightforward way.

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