24. Make Sense and Persevere What is the least number of points you must plot to have examples of all four sets of numbers, including at least one positive integer and one negative integer? Explain.

To ensure that you have examples of all four sets of numbers—natural numbers, whole numbers, integers, and rational numbers—you need to consider the definitions of each set: 1. **Natural Numbers (N)**: These are the positive integers starting from 1 (1, 2, 3, ...). 2. **Whole Numbers (W)**: These include all natural numbers plus zero (0, 1, 2, 3, ...). 3. **Integers (Z)**: These include all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...). 4. **Rational Numbers (Q)**: These are numbers that can be expressed as a fraction of two integers, including integers, fractions, and terminating or repeating decimals. To meet the requirement of having at least one positive integer and one negative integer, we can choose the following points: 1. **Positive Integer**: Choose 1 (which is a natural number, whole number, and integer). 2. **Negative Integer**: Choose -1 (which is an integer). 3. **Whole Number**: Choose 0 (which is a whole number and an integer). 4. **Rational Number**: Choose a fraction, such as 1/2 (which is a rational number). Now, let's summarize the points we have chosen: - **1**: Positive integer (natural number, whole number, integer) - **-1**: Negative integer (integer) - **0**: Whole number (also an integer) - **1/2**: Rational number With these four points, we have examples of all four sets of numbers, including at least one positive integer (1) and one negative integer (-1). Thus, the least number of points you must plot to have examples of all four sets of numbers is **4**.