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Chapter 0: Problem 42

Simplify each expression. $$ -\frac{5}{6}(18 w)(5 z) $$

Short Answer

Expert verified
-75wz

Step by step solution

01

Multiply the Constants

First, multiply the constants -\( \frac{5}{6} \), 18, and 5. \[ -\frac{5}{6} \times 18 \times 5 \]
02

Simplify the Multiplication of Constants

Calculate the product of these constants step by step. First, multiply -\( \frac{5}{6} \) and 18: \[ -\frac{5}{6} \times 18 = -15 \]Then, multiply -15 by 5: \[ -15 \times 5 = -75 \]
03

Multiply the Variables

Now, multiply the remaining variables (\( w \) and \( z \)). The expression becomes: \[ -75wz \]

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Key Concepts

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

Multiplication of Constants
When simplifying algebraic expressions, one of the initial steps often involves multiplying constants. This means you focus on the numerical coefficients first, before dealing with any variables. In the given exercise, you have three constants to multiply: -\(\frac{5}{6}\), 18, and 5. Start by multiplying -\(\frac{5}{6}\) by 18. This translates into: \ -\(\frac{5}{6} \times 18 = -15\).
Next, multiply -15 by 5 to get: \ -\(15 \times 5 = -75\).
These constants give the final simplified value of -75.
Simplifying Expressions
Simplifying algebraic expressions involves reducing them to their simplest form. This often means combining all constants and like terms to make the expression more manageable.
In the exercise, after multiplying constants, we are left with -75. Next, we need to ensure all variables are properly included in the simplified expression, which leads us to the next step.
In simplifying expressions, always remember to:
  • Handle constants first.
  • Then deal with the variables.
  • Combine those results for the simplest form.

This approach ensures you don't overlook any part of the expression.
Combining Like Terms
Combining like terms is a crucial step in simplifying algebraic expressions. 'Like terms' are terms that have the same variables raised to the same power. The coefficients of such terms can be added or subtracted.
In our example, the terms are: -75, w, and z. Since -75 is a constant and w and z are variables, there are no like terms to combine here.
However, the final combined and simplified expression is -75wz. This consolidates the numerical and variable parts effectively.
  • Combine constants with constants.
  • Combine variable terms with the same exponents.
Following these steps ensures clarity and correctness in your final expression.

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