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Chapter 2: Problem 78

Fill in the blank with \(<,>,\) or \(=\) $$-8 \square-10$$

Short Answer

Expert verified
-8 > -10

Step by step solution

01

Understand the Problem

The problem is asking to compare -8 and -10 using one of the symbols: <, >, or =. This means we need to determine which number is greater or if they are equal.
02

Compare the Magnitude

When dealing with negative numbers, the number with a lower absolute value is considered to be the greater number. Since the absolute value of -8 is 8 and the absolute value of -10 is 10, -8 has a lower absolute value compared to -10.
03

Determine the Relationship

Given that -8 has a smaller absolute value than -10, -8 is greater than -10. Therefore, the symbol that correctly compares these numbers is >.

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Key Concepts

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

Inequalities
Inequalities are expressions that show the relationship between two values. Common inequality symbols include \(<\) (less than), \(>\) (greater than), and \(=\) (equal to). When comparing two numbers, the symbol indicates whether one number is smaller, larger, or the same as the other. For example, in the equation \(-8 \, \square \, -10\), we must decide which inequality symbol to use. Here, determining which number is greater involves looking at their values and understanding the rules for inequalities & negative numbers.
Negative Numbers
Negative numbers are numbers less than zero, represented by a minus sign (\(-\)). They are often used to show a decrease or a deficit. When comparing negative numbers, the number closer to zero is considered greater because it represents a smaller magnitude of a negative value. For instance, between \(-8\) and \(-10\), \(-8\) is closer to zero. So, \(-8\) is greater than \(-10\).
To compare negative numbers, always think about their position on the number line. The number further to the right is greater.
Absolute Value
Absolute value represents the distance a number is from zero, regardless of direction. It's denoted by vertical bars, like so: \(|a|\). For example, \(|-8| = 8\) and \(|-10| = 10\). Absolute value helps in understanding the magnitude of a number without considering whether it is positive or negative.
When comparing two negative numbers, you can look at their absolute values: the number with the smaller absolute value is actually the larger negative number. That's why \(-8\) (with an absolute value of 8) is greater than \(-10\) (with an absolute value of 10).

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Most popular questions from this chapter

Find the range. The range of a set of numbers is the difference between the highest value and the lowest value. That is, range = highest - lowest. Find two integers whose difference is \(-6 .\) Answers may vary.

Fill in the blank with \(<,>,\) or \(=\) $$-|22| \square 0$$

Divide the real numbers, if possible. $$\frac{-48}{-3}$$

Simplify. $$(-5)^{4}$$

Divide the real numbers, if possible. $$\frac{-56}{-8}$$
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