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Chapter 2: Problem 79

Fill in the blank with \(<,>,\) or \(=\) $$-44 \square-54$$

Short Answer

Expert verified
-44 > -54.

Step by step solution

01

- Understand the Numbers

The numbers given in the problem are -44 and -54. Both numbers are negative.
02

- Compare Magnitudes

Ignore the negative sign for a moment and compare the magnitudes of the numbers. The number 44 is less than 54.
03

- Apply the Negative Sign

Since both numbers are negative, the number with the greater magnitude is actually the smaller number. Therefore, -44 is greater than -54.
04

- Fill in the Blank

Using the comparison from the previous step, fill in the blank with the correct symbol: -44 > -54.

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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 that are less than zero. They have a minus sign (-) before them. When comparing negative numbers, it's important to remember that they behave differently from positive numbers. The more negative a number is, the smaller its value. For example, -10 is less than -5 because -10 is further from zero on the number line.

Negative numbers are very useful in many real-life scenarios, such as calculating temperatures below freezing, representing debts, or describing elevations below sea level. Understanding how to properly compare and work with negative numbers is crucial for solving many mathematical problems.
Number Magnitude
The magnitude of a number is its absolute value, which means how far the number is from zero on the number line, regardless of its sign. For instance, both 44 and -44 have the same magnitude of 44. Therefore, when comparing numbers based on magnitude, you ignore the signs and compare the absolute values.

In the given example, we have -44 and -54. To compare their magnitudes, we look at 44 and 54. Since 44 is less than 54, -44 has a smaller magnitude than -54. However, when we apply the negative signs back, the comparison reverses, because numbers with larger magnitudes are actually smaller when they are negative. Hence, -44 is greater than -54 in value.
Using Inequality Symbols
Inequality symbols are used to compare two numbers or quantities. The main inequality symbols are:

  • <: less than
  • >: greater than
  • =: equal to
  • 鈮�: less than or equal to
  • 鈮�: greater than or equal to


In mathematics, choosing the correct inequality symbol is crucial for showing the relationship between numbers. In the exercise provided, we need to compare -44 and -54. From our understanding of negative numbers and their magnitudes, -44 is greater than -54. Therefore, the correct symbol to use is >, resulting in -44 > -54.

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Most popular questions from this chapter

Simplify. $$25-13-(-40)$$

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

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 \(-20 .\) Answers may vary.

Fill in the blank with \(<,>,\) or \(=\) $$-|32| \square|0|$$

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