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Chapter 2: Problem 24

Insert \(<\) or \(>\) between each pair of integers to make a true statement. $$ -8 \quad 0 $$

Short Answer

Expert verified
-8 < 0

Step by step solution

01

Understand the Problem

We need to compare two integers: -8 and 0. Our task is to determine which is greater and insert the appropriate inequality sign between them.
02

Identify the Numbers on the Number Line

Consider the number line. We represent numbers with 0 at the center and negative numbers on the left while positive numbers are on the right. Here, -8 is located to the left of 0.
03

Determine the Inequality

Since -8 is to the left of 0 on the number line, it means that -8 is less than 0. Therefore, we insert the symbol '<' between -8 and 0.

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Key Concepts

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

Integers
Integers are a fundamental part of mathematics. They are whole numbers, meaning they do not include any decimals or fractions. Integers can be positive, negative, or zero. Here are some important points about integers:
  • Positive integers: These are numbers greater than zero, such as 1, 2, 3, and so on.
  • Negative integers: These are numbers less than zero, like -1, -2, -3, etc.
  • Zero: This is a special integer that is neither positive nor negative.
Understanding integers is crucial for learning number line concepts, where integers are placed in relation to one another.
Inequality Symbols
Inequality symbols are useful tools in mathematics that help compare values. They tell us if one number is larger, smaller, or equal to another. Here are some of the basic inequality symbols and what they mean:
  • \( < \): This symbol means 'less than.' We use it to show that the number on the left is smaller than the number on the right.
  • \( > \): This symbol stands for 'greater than.' It's used to indicate that the number on the left is bigger than the number on the right.
  • \( = \): Although not directly an inequality symbol, it means two numbers are 'equal.'
When working with inequalities, it's important to compare numbers accurately, especially when dealing with negative and positive numbers. This will help you decide the correct symbol to use.
Negative Numbers
Negative numbers are integers that are less than zero. They play a crucial role in mathematics, especially when comparing values on a number line. Here are some key facts about negative numbers:
  • Negative numbers are always to the left of zero on the number line. This positioning indicates that they are smaller than any positive number.
  • As you move further left along the number line, the value of negative numbers decreases (e.g., -3 is greater than -8).
  • Negative numbers often represent concepts such as loss or deficiency, like in financial amounts when you owe money.
Comprehending the order and placement of negative numbers can simplify the process of determining inequalities, making it easier to understand how and when one negative number is smaller or larger than another.

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Most popular questions from this chapter

The temperature on one January day in Minneapolis was \(10^{\circ}\) below \(0^{\circ}\) Celsius. Represent this quantity by an integer and tell whether this temperature is cooler or warmer than \(5^{\circ}\) below \(0^{\circ}\) Celsius.

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Evaluate each expression for \(x=-3\) and \(z=-4\) $$ 2 z^{3} $$

Find the opposite of each integer. $$ 23 $$

Multiply or divide as indicated. $$ \frac{96}{3} $$
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