/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 The quotient of a number and \(-... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 48

The quotient of a number and \(-2.5\) is \(2.72 .\) Find the number.

Short Answer

Expert verified
The number is -6.8.

Step by step solution

01

Set up the Equation

Translate the word problem into a mathematical equation. If the number is denoted by \( x \), the quotient of a number and \(-2.5\) is given by \( \frac{x}{-2.5} = 2.72 \).
02

Isolate the Variable

To find the value of \( x \), multiply both sides of the equation by \(-2.5\) to isolate \( x \). \( \frac{x}{-2.5} \times -2.5 = 2.72 \times -2.5 \)
03

Simplify

Simplify the equation to solve for \( x \). \( x = 2.72 \times -2.5 \).
04

Calculate the Result

Perform the multiplication to find the value of \( x \). \( x = -6.8 \).

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Key Concepts

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

quotient
In mathematics, the term 'quotient' represents the result of division. For example, in the exercise, the quotient is the result of dividing a number by -2.5, resulting in 2.72. Understanding quotients is crucial, as it helps us to interpret problems and set up equations correctly.
isolate variable
To solve equations, we often need to isolate the variable. In this exercise, our goal is to find the unknown value of the number. We begin by setting up the equation where the unknown number is represented by \(x\). The given equation is \frac{x}{-2.5} = 2.72. By multiplying both sides by -2.5, we isolate \(x\), making it easier to solve for the variable. Isolating the variable simplifies the problem and sets the stage for the next steps.
simplify equations
Simplifying equations means to make them easier to understand or solve. After isolating the variable, we have the equation \(x = 2.72 \times -2.5\). This step involves performing the arithmetic operation to simplify the equation. By simplifying, we reduce the complexity and make it easier to calculate the final result. In our case, multiplication helps us simplify the equation to the point where we can find that \(x = -6.8\). Simplifying equations is a powerful tool in mathematics, ensuring we arrive at clear and concise answers.
multiplication
Multiplication is a fundamental arithmetic operation used frequently in solving equations. In this exercise, after isolating the variable \(x\), we are required to multiply 2.72 by -2.5 to find the value of \(x\). This calculation, 2.72 \times -2.5, results in -6.8. Multiplication helps us transform and evaluate equations, making it an essential skill for solving mathematical problems. Mastering multiplication can significantly enhance one's ability to tackle diverse mathematical challenges.

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Most popular questions from this chapter

For Exercises \(83-88\) simplify by $$(78.2-60.2) \div \frac{9}{13}$$

For Exercises \(83-88\) simplify by $$6.5+\frac{1}{8}\left(\frac{1}{5}\right)^{2}$$

For Exercises \(85-90,\) refer to the table. The table gives the closing stock prices (in dollars per share) for the first day of trading for the given month. $$\begin{array}{l|c|c|c|c|c} \text { Stock } & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\ \hline \text { IBM } & \$ 97.27 & \$ 99.00 & \$ 92.27 & \$ 95.21 & \$ 103.17 \\\ \hline \text { FedEx } & \$ 109.77 & \$ 111.89 & \$ 114.16 & \$ 106.07 & \$ 106.11 \\ \hline \end{array}$$ Between which two consecutive months did the IBM stock increase the most? What was the amount of increase?

Which number is between 42.73 and 42.86? Circle all that apply. a. 42.81 b. 42.64 c. 42.79 d. 42.85

An outdoor torch lamp shines light a distance of \(30 \mathrm{ft}\) in all directions. What is the total ground area lighted?
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