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Chapter 0: Problem 48

Determine whether statement is true or false. \(-3>-13\)

Short Answer

Expert verified
The statement \(-3>-13\) is true.

Step by step solution

01

Understanding the rule of inequality between negative numbers

In inequality, a negative number is always smaller than a positive number. For two negative numbers, the number with the less absolute value is greater. So, in our problem, \(-3\) has a smaller absolute value than \(-13\).
02

Comparing -3 with -13

\(-3\) is greater than \(-13\) because it has a less absolute value than \(-13\) in the negative number range. This does confirm the initial statement.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers that are less than zero. They are found on the left side of the number line. While positive numbers move to the right, negative numbers increase in value as they move to the left. This can sometimes be confusing because, with negative numbers, a number that looks larger actually represents a smaller value.

Here are some key points about negative numbers:
  • Negative numbers are denoted with a minus (-) sign in front of them, like (-3) or (-13).
  • On a number line, (-3) is to the right of (-13), hence (-3) is greater than (-13).
  • When comparing two negative numbers, the one with the lower absolute value is considered greater. For example, between (-3) and (-13), (-3) is greater.
Absolute Value
Absolute value is a concept that helps us understand how far a number is from zero on the number line, regardless of direction. The absolute value of a number is always non-negative. This is crucial when dealing with inequalities, especially with negative numbers.

Some important facts about absolute value include:
  • The absolute value of a number is denoted by two vertical bars surrounding the number, like \(|-3| = 3\) or \(|-13| = 13\).
  • For negative numbers, you ignore the negative sign and take the number as positive for calculating the absolute value.
  • Comparing absolute values can help determine which of two negative numbers is "larger" or "smaller," where a smaller absolute value means a greater actual value with negative numbers.
Comparing Numbers
Comparing numbers involves determining which number is greater or smaller. This can be straightforward with positive numbers but becomes a bit trickier with negative numbers due to their position on the number line.

When comparing numbers, consider the following:
  • For positive numbers, a larger number compared to another means a greater value.
  • For negative numbers, a number with a larger absolute value is less than a number with a smaller absolute value, because it is further to the left on the number line.
  • Thus, when comparing (-3) and (-13), since (-3) has a smaller absolute value than (-13), (-3) is greater in actual value.
By understanding these principles, students can effectively compare both negative and positive numbers in different contexts.

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