1. Let's start by understanding the problem: we want to practice elementary operations (addition, subtraction, multiplication, division) and ordering (comparing sizes) between integers, rational numbers, and real numbers. 2. **Definitions:** - Integers are whole numbers including negatives, zero, and positives, e.g., $-3, 0, 4$. - Rational numbers are numbers that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$, e.g., $\frac{1}{2}, -\frac{3}{4}$. - Real numbers include all rational and irrational numbers (numbers that cannot be expressed as fractions, like $\sqrt{2}$ or $\pi$). 3. **Elementary operations:** - Addition: $a + b$ - Subtraction: $a - b$ - Multiplication: $a \times b$ - Division: $\frac{a}{b}$, where $b \neq 0$ 4. **Ordering rules:** - For any two numbers $a$ and $b$, if $a < b$, then $a$ is less than $b$. - Ordering applies to integers, rationals, and real numbers. 5. **Example practice:** - Add integers: $3 + (-5) = -2$ - Multiply rationals: $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ - Compare real numbers: $\sqrt{2} \approx 1.414$ and $\frac{3}{2} = 1.5$, so $\sqrt{2} < \frac{3}{2}$ 6. To practice, try problems like: - Calculate $-7 + 12$ - Simplify $\frac{5}{6} - \frac{1}{3}$ - Determine if $-2.5$ is greater or less than $-3$ This approach will help you understand operations and ordering across these number sets.