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Chapter 1: Problem 59

Evaluate each of the following expressions, if possible. $$\frac{9(-6)}{9-6}$$

Short Answer

Expert verified
-18.

Step by step solution

01

- Simplify the numerator

Multiply 9 by -6 in the numerator. The expression becomes: The simplified numerator is formatter non 猫 formattato LaTex The expression is simplified to: -54.
02

- Simplify the denominator

Subtract 6 from 9 in the denominator. 9 - 6 = 3.
03

- Divide the results

Divide the simplified numerator by the simplified denominator. -54 梅 3 = -18.

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Key Concepts

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

Numerator and Denominator
In fractions, the numerator is the top number, and the denominator is the bottom number. The numerator represents how many parts we have, while the denominator tells us into how many parts the whole is divided. For example, in the fraction \( \frac{3}{4} \), 3 is the numerator, and 4 is the denominator.
Understanding these parts is essential for simplifying fractions because it helps us know what operations to perform.
When simplifying, keep these key points in mind:
  • Always perform operations on the numerator and denominator separately first.
  • Your final answer should maintain the same numerator and denominator format.
Multiplication in Algebra
Multiplication in algebra works similarly to basic arithmetic but often involves variables. For instance, if you have \( 9(-6) \), you need to multiply 9 by -6. This multiplication is straightforward because there are no variables here. Let's walk through it:
  • First, multiply the absolute values: \( 9 \times 6 = 54 \).
  • Next, apply the sign rule: a positive times a negative yields a negative. So, \( 9 \times -6 = -54 \).
Now you have the simplified numerator as -54. This clear separation of steps ensures that students don't get confused.
Division in Algebra
Division in algebra often follows simplification of both the numerator and the denominator. Continuing from our example, we have \( \frac{-54}{3} \). Here鈥檚 how to approach it:
  • First, ensure the numerator (-54) and denominator (3) are in their simplest form.
  • Second, divide the absolute values: \( 54 \div 3 = 18 \).
  • Third, apply the sign rule: a negative divided by a positive results in a negative. So, \( \frac{-54}{3} = -18 \).
With these steps, the fraction simplifies neatly to -18, ensuring you understand how division works in algebraic contexts.

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Most popular questions from this chapter

In Exercises \(73-84\), evaluate the given expression. $$9-5 \cdot 4-2$$

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In Exercises \(73-84\), evaluate the given expression. $$9-(5 \cdot 4-2)$$
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