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Chapter 2: Problem 22

Evaluate each expression. $$\frac{x}{-5}, \text { if } x=-85$$

Short Answer

Expert verified
The value of \(\frac{x}{-5}\) when \(x = -85\) is 17.

Step by step solution

01

Substitute the Value of x

Replace the variable \(x\) in the expression \(\frac{x}{-5}\) with the given value \(-85\). This gives us \(\frac{-85}{-5}\).
02

Perform the Division

Divide the numerator \(-85\) by the denominator \(-5\). Remember that dividing two negative numbers results in a positive number, so \(\frac{-85}{-5} = 17\).

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Key Concepts

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

Expression Evaluation
When we talk about expression evaluation, we're essentially trying to simplify a mathematical statement to find its value. This involves following specific mathematical rules, such as the order of operations, to break down the expression into something more understandable. In this exercise, the expression given is \(\frac{x}{-5}\).
The goal is to evaluate this expression by replacing any variables with given numbers. Once substituted, you'll perform any mathematical operations contained within the expression, such as addition, subtraction, multiplication, or division. Always pay close attention to the signs of numbers and the operations between them!
Negative Number Division
Dividing negative numbers can be tricky, but with some tips, it gets easier. Imagine dividing a negative number by another negative number. A common rule of thumb is:
  • Negative 梅 Negative = Positive
  • Negative 梅 Positive = Negative
  • Positive 梅 Negative = Negative
In the exercise, after substituting for the variable, you have the division \(\frac{-85}{-5}\).
Both the numerator and the denominator are negative. Thus, the result of dividing \(-85\) by \(-5\) is a positive number, which is \(17\). Understanding how signs work in division is crucial to arriving at the correct answer.
Variable Substitution
Variable substitution involves replacing a variable with a given number in a mathematical expression. This is often one of the first steps when evaluating expressions with variables. In the exercise, the variable is \(x\).
We are told to replace \(x\) with \(-85\). So, the original expression \(\frac{x}{-5}\) becomes\(\frac{-85}{-5}\).
This substitution is a critical step as it transforms the expression from an abstract form into something concrete that can be evaluated further. Always ensure that you substitute correctly before proceeding with other calculations.
Step-by-step Problem Solving
Breaking down a problem into steps makes solving it much easier. In this case, we're evaluating an expression in a few simple steps:
  • Step 1: Substitute the variable with the given number. Turn \(\frac{x}{-5}\) into \(\frac{-85}{-5}\).
  • Step 2: Perform the division. Divide \(-85\) by \(-5\), remembering that the result will be positive since dividing two negative numbers yields a positive result.
Thinking through each part of the process and tackling it bit by bit helps prevent mistakes and ensures that you understand each part of the problem. It is a key strategy not just in prealgebra but also in more advanced mathematics.

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Most popular questions from this chapter

At 8: 00 P.M., a temperature of \(78^{\circ} \mathrm{F}\) was recorded. The temperature then changed at an average rate of \(-2^{\circ} \mathrm{F}\) per hour for a 15 -hour period. What was the temperature in degrees Fahrenheit at 7: 00 A.M.?

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