Problem 80
Question
True or False: All negative numbers are smaller than all positive numbers.
Step-by-Step Solution
Verified Answer
True. Every negative number is smaller than any positive number.
1Step 1: Understanding Negative and Positive Numbers
First, we understand that negative numbers are all numbers less than zero, represented with a negative sign (-). Positive numbers are greater than zero and are represented with no sign (or a positive sign). For example, -5 is a negative number, and 3 is a positive number.
2Step 2: Compare Negative Numbers with Positive Numbers
The number zero separates positive and negative numbers on the number line. Every positive number is to the right of zero, and every negative number is to the left of zero. Thus, any negative number is to the left of any positive number on the number line.
3Step 3: Conclusion from Number Line Analysis
Given the number line positioning, negative numbers are always to the left of positive numbers, indicating they are smaller. Hence, every negative number is indeed smaller than any positive number.
Key Concepts
Number LineNegative NumbersPositive Numbers
Number Line
A number line is a visual tool used to represent numbers in order. It extends infinitely in both directions horizontally. Generally, we place zero in the middle. From zero, numbers increase positively to the right and decrease negatively to the left.
Using a number line, we can easily compare numbers. Any number positioned to the left of another number is considered smaller. Conversely, numbers to the right are larger. This simple left-and-right rule helps us visualize and determine the size of numbers quickly.
Number lines are especially useful when teaching concepts related to negative and positive numbers. It provides a clear, visual representation that makes comparison straightforward and intuitive.
Using a number line, we can easily compare numbers. Any number positioned to the left of another number is considered smaller. Conversely, numbers to the right are larger. This simple left-and-right rule helps us visualize and determine the size of numbers quickly.
Number lines are especially useful when teaching concepts related to negative and positive numbers. It provides a clear, visual representation that makes comparison straightforward and intuitive.
Negative Numbers
Negative numbers are numbers that are less than zero. They are represented with a minus or negative sign (-) before them. For example, -1, -5, and -10 are all negative numbers.
These numbers are found left of zero on the number line. This placement shows that negative numbers are lower in value than positive numbers and zero itself. It’s essential to remember that the more negative a number, the smaller its value. For instance, -10 is smaller than -5.
Negative numbers are commonly found in situations involving losses, below-zero temperatures, or any other context where values decrease or fall.
These numbers are found left of zero on the number line. This placement shows that negative numbers are lower in value than positive numbers and zero itself. It’s essential to remember that the more negative a number, the smaller its value. For instance, -10 is smaller than -5.
Negative numbers are commonly found in situations involving losses, below-zero temperatures, or any other context where values decrease or fall.
Positive Numbers
Positive numbers are all numbers greater than zero. They are usually written without a sign but sometimes with a plus (") sign. For example, 2, 15, or +7.
On the number line, positive numbers lie to the right of zero. This position indicates that positive numbers are always larger than negative numbers and zero. It's important to see positive numbers in various aspects of daily life, such as in counts of items, measurements above sea level, or profits.
Understanding positive numbers is crucial for performing arithmetic operations and solving real-world problems efficiently.
On the number line, positive numbers lie to the right of zero. This position indicates that positive numbers are always larger than negative numbers and zero. It's important to see positive numbers in various aspects of daily life, such as in counts of items, measurements above sea level, or profits.
Understanding positive numbers is crucial for performing arithmetic operations and solving real-world problems efficiently.
Other exercises in this chapter
Problem 80
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