Test Questions on Rational Numbers: Prepare for Your 8th Grade Exam

📚 Quick Study Guide

• 🔢 Definition: Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
• ➕ Addition/Subtraction: To add or subtract rational numbers, they must have a common denominator. If $\frac{a}{c}$ and $\frac{b}{c}$ are rational numbers, then $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ and $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$.
• ✖️ Multiplication: To multiply rational numbers, multiply the numerators and the denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.
• ➗ Division: To divide rational numbers, multiply by the reciprocal of the divisor: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$.
• ⚖️ Properties: Rational numbers follow the commutative, associative, and distributive properties of real numbers.
• 💯 Decimal Representation: Rational numbers can be expressed as terminating or repeating decimals.

📝 Practice Quiz

1. What is the result of $\frac{2}{5} + \frac{1}{5}$?
   1. $\frac{3}{10}$
   2. $\frac{2}{25}$
   3. $\frac{3}{5}$
   4. $\frac{1}{2}$
2. What is the result of $\frac{3}{4} - \frac{1}{2}$?
   1. $\frac{2}{2}$
   2. $\frac{1}{4}$
   3. $\frac{2}{4}$
   4. $\frac{1}{8}$
3. What is the result of $\frac{2}{3} \times \frac{3}{4}$?
   1. $\frac{5}{7}$
   2. $\frac{6}{12}$
   3. $\frac{1}{2}$
   4. $\frac{5}{12}$
4. What is the result of $\frac{1}{2} \div \frac{1}{4}$?
   1. $\frac{1}{8}$
   2. $2$
   3. $\frac{1}{2}$
   4. $\frac{3}{4}$
5. Which of the following is NOT a rational number?
   1. $0$
   2. $\sqrt{2}$
   3. $\frac{1}{3}$
   4. $-5$
6. Convert $\frac{3}{8}$ to a decimal.
   1. $0.3$
   2. $0.375$
   3. $0.83$
   4. $2.67$
7. Which fraction is equivalent to $0.75$?
   1. $\frac{1}{4}$
   2. $\frac{1}{2}$
   3. $\frac{2}{3}$
   4. $\frac{3}{4}$