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Chapter 2: Problem 113

Answer true or false. A positive number is always greater than a negative number.

Short Answer

Expert verified
True, a positive number is always greater than a negative number.

Step by step solution

01

Define Positive Numbers

Positive numbers are numbers greater than zero. Examples include 1, 2, 3,... and so on. Positive numbers represent a quantity greater than zero.
02

Define Negative Numbers

Negative numbers are numbers less than zero. Examples include -1, -2, -3,... and so on. Negative numbers represent a quantity less than zero.
03

Compare Positive and Negative Numbers

Since positive numbers are greater than zero and negative numbers are less than zero, any positive number will always be greater than any negative number, as it lies to the right of zero on the number line, whereas negative numbers lie to the left.

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Key Concepts

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

Number Line
To better understand positive and negative numbers, we can use a number line as a visual tool. A number line is a straight line with numbers placed along it at equal intervals.
  • The center of the number line is zero.
  • Numbers to the right of zero are positive.
  • Numbers to the left are negative.
This arrangement helps us see that, as we move to the right on the number line, the numbers increase. The further right a number is, the larger it is.
When you move left from zero, you'll notice numbers decrease, showing that they are getting smaller.
Therefore, this visualization makes it clear that any positive number, situated to the right, is larger than any negative number, which lies to the left.
Comparing Numbers
Comparing numbers using a number line is a straightforward process. When we have two numbers and we want to determine which is greater, the number closer to the right is the larger one. Consider the following:
  • Any positive number (e.g., 3) is greater than any negative number (e.g., -2). This is because 3 is to the right of 0 and thus to the right of -2.
  • If you compare 2 and -4, 2 is greater. Again, 2 lies to the right.
An easy way to visualize it:

Imagine you are standing on a number line. Step right (towards positive numbers) or left (towards negative numbers) to compare. The direction towards the right always points to larger numbers compared to those on the left.
Integer Properties
Understanding integer properties is key to comparing positive and negative numbers. Integers include both positive and negative numbers, as well as zero. They are whole numbers and do not have fractions.
  • Positive Integers: These are numbers like 1, 2, 3. They are greater than zero.
  • Negative Integers: These are numbers like -1, -2, -3. They are less than zero.
  • Zero: It is neutral. It is neither positive nor negative and is the dividing point on a number line.
When comparing integers:

- Positive integers are always greater than zero, making them superior to negative integers by default.

- Negative integers are always less than zero, placing them lower on the number line compared to any positive number.
Thus, understanding the nature and order of integers simplifies any comparative analysis between different numbers.

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