8th Grade Real Number System Review Questions with Answers

📚 Quick Study Guide

• 🔢 Real Numbers: Include all rational and irrational numbers.
• ➕ Rational Numbers: Can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. This includes integers, fractions, terminating decimals, and repeating decimals.
• ♾️ Irrational Numbers: Cannot be expressed as a fraction. Their decimal representations are non-terminating and non-repeating (e.g., $\pi$, $\sqrt{2}$).
• 📏 Integers: Whole numbers and their negatives (e.g., -3, -2, -1, 0, 1, 2, 3).
• 💯 Whole Numbers: Non-negative integers (e.g., 0, 1, 2, 3...).
• 🌱 Natural Numbers: Positive integers (e.g., 1, 2, 3...).
• 🧮 Key Properties:
  • Commutative Property: $a + b = b + a$ and $a \cdot b = b \cdot a$
  • Associative Property: $(a + b) + c = a + (b + c)$ and $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
  • Distributive Property: $a \cdot (b + c) = a \cdot b + a \cdot c$

📝 Practice Quiz

1. What type of number is $\sqrt{9}$?
   1. Irrational
   2. Rational
   3. Imaginary
   4. Transcendental
2. Which of the following is an irrational number?
   1. $\frac{1}{3}$
   2. 0.25
   3. $\sqrt{5}$
   4. -7
3. Which property is demonstrated by the equation $3 + 5 = 5 + 3$?
   1. Associative Property of Addition
   2. Commutative Property of Addition
   3. Distributive Property
   4. Identity Property of Addition
4. Which set of numbers does $\frac{4}{0}$ belong to?
   1. Rational Numbers
   2. Integers
   3. Real Numbers
   4. Undefined
5. What is the decimal representation of $\frac{2}{3}$?
   1. 0.6
   2. 0.67
   3. 0.$\overline{6}$
   4. 0.7
6. Which of the following is an integer but not a whole number?
   1. 0
   2. 5
   3. -3
   4. $\frac{1}{2}$
7. Which property justifies the statement $2(x + 3) = 2x + 6$?
   1. Commutative Property of Multiplication
   2. Associative Property of Multiplication
   3. Distributive Property
   4. Identity Property of Multiplication