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Chapter 1: Problem 65

List three integers between -20 and -5 .

Short Answer

Expert verified
Three possible integers are -18, -15, -12.

Step by step solution

01

Understanding the Problem

We need to identify three integers that fall between the integers -20 and -5. The problem requires that these integers be strictly greater than -20 and less than -5.
02

Identifying the Range

The integers we are looking for must be within the range of (-20, -5), meaning the boundaries are not included. Our eligible integers are -19, -18, ..., -6.
03

Selecting Three Integers

Among the integers in our set {-19, -18, ..., -6}, select any three. For instance, we can choose -18, -15, and -12.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers less than zero and are represented with a minus sign, such as -1, -2, and so on. They are an essential part of the number line, located to the left of zero. Understanding negative numbers is crucial, as they appear in various real-world contexts, such as temperatures below freezing or bank overdrafts.
  • In mathematics, operations with negative numbers follow these rules: adding a negative number is like subtraction, and subtracting a negative number is like addition.
  • When multiplying or dividing, two negative numbers result in a positive number, whereas a positive and negative product or quotient results in a negative number.
By mastering these concepts, tackling problems involving negative numbers becomes more logical and straightforward.
Exploring the Range in Mathematics
A range in mathematics denotes the span between two points, detailing all possible values or elements within these boundaries. When discussing numbers, particularly integers, the range often helps to define the scope of your answer, as seen between two specific limits like -20 and -5.
  • An open range (a, b) does not include the endpoints, meaning any value strictly greater than 'a' and less than 'b' is part of the range.
  • When a range is closed, [a, b], it includes both endpoints.
In the given exercise, the range (-20, -5) is open, so neither -20 nor -5 are included. This understanding helps narrow down possible answers in mathematics.
Selecting Integers within a Range
Selecting integers is a systematic process of choosing whole numbers, either from a set list or within a defined mathematical range. In the range (-20, -5), selecting integers involves picking numbers that fall strictly between -20 and -5.
  • The integers within this range can be written in sequence: **-19, -18, ..., -6**.
  • From these, any combination of three numbers can be chosen, such as **-18, -15, and -12** or any other trio.
The key lies in ensuring that selected integers adhere to the range's conditions, remaining strictly bound by the limits provided, ensuring that answers align with the problem's context. Understanding this concept helps in accurately solving range-related questions.

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