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Chapter 5: Problem 47

The quotient of a number and 5 is \(-1.88 .\) Find the number.

Short Answer

Expert verified
The number is -9.4.

Step by step solution

01

Identify the Given Information

The quotient of a number and 5 is -1.88. This can be written as the equation \ \[ \frac{x}{5} = -1.88 \].
02

Set Up the Equation

Rewrite the given information as an algebraic equation: \ \[ \frac{x}{5} = -1.88 \].
03

Solve for the Unknown Variable

To find the value of x, multiply both sides of the equation by 5: \ \[ x = -1.88 \times 5 \].
04

Perform the Multiplication

Calculate: \ \[ -1.88 \times 5 = -9.4 \]. Thus, \ \[ x = -9.4 \].
05

Conclusion

The number is \ \[ -9.4 \].

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Key Concepts

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

algebraic equations
An algebraic equation is a mathematical statement that uses variables and numbers combined by operations like addition, subtraction, multiplication, and division. In our exercise:
\[\frac{x}{5} = -1.88 \]
This is an algebraic equation in which a number divided by 5 equals -1.88.
Understanding algebraic equations is crucial because they help us describe relationships and solve for unknown variables. These equations come in different forms: linear, quadratic, and more. By manipulating equations, we can find the value of an unknown variable that makes the equation true.
unknown variable
An unknown variable is a symbol that represents a number we don't know yet. In math, it's often called 'x,' 'y,' or any other letter. In our exercise, 'x' is the unknown variable:
\[\frac{x}{5} = -1.88 \]
Here, 'x' stands for the number we're trying to find. Identifying the unknown variable is the first step in solving any algebraic equation. We use known values and operations to isolate this variable and figure out its value. This process transforms an abstract problem into a concrete solution.
Always remember: the goal is to solve the equation by isolating the unknown variable on one side.
multiplication in algebra
Multiplication in algebra is a key operation that helps us simplify equations and solve for unknowns. In our example, we used multiplication to find 'x':
\[\frac{x}{5} = -1.88 \]
To isolate 'x,' we multiplied both sides by 5:
\[ x = -1.88 \times 5 \]
Multiplying both sides by the same number keeps the equation balanced. This is a fundamental rule in algebra: whatever you do to one side of the equation, you must do to the other.
\[-1.88 \times 5 = -9.4 \]
Hence, 'x' is -9.4. Multiplication simplifies the problem and brings us closer to finding our answer.

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Most popular questions from this chapter

Perform the indicated operations. $$0 . \overline{5} \div 0 . \overline{2}-0.75$$

Water flows into a pool at a constant rate. The water level is recorded at several 1-hr intervals. a. From the table, how many inches is the water level rising each hour? b. At this rate, what will the water level be at 1: 00 PM.? c. At this rate, what will the water level be at 3.00 p.M.? $$\begin{array}{c|c} \text { Time } & \text { Water Level } \\ \hline 9: 00 \mathrm{A} . \mathrm{M} & 4.2 \mathrm{in} . \\ \hline 10: 00 \mathrm{A} \ldots & 5.9 \mathrm{in} . \\ \hline 11.00 \mathrm{A} \ldots & 7.6 \mathrm{in} . \\ \hline 12.00 \mathrm{em} . & 9.3 \mathrm{in.} \\ \hline \end{array}$$

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