Quiz on adding, subtracting, multiplying, and dividing rational numbers

📚 Quick Study Guide

• 🔢 A rational number can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
• ➕ To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the same denominator: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$.
• ➖ To add or subtract rational numbers with different denominators, find a common denominator, convert each fraction to an equivalent fraction with the common denominator, and then add or subtract the numerators.
• ✖️ To multiply rational numbers, multiply the numerators and multiply the denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.
• ➗ To divide rational numbers, multiply by the reciprocal of the divisor: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$.
• 💡 Remember to simplify your answers to the lowest terms.
• ✔️ When adding/subtracting negative rational numbers, remember the rules for adding/subtracting negative numbers.

📝 Practice Quiz

1. What is $\frac{1}{4} + \frac{2}{4}$?
   1. $\frac{1}{8}$
   2. $\frac{3}{8}$
   3. $\frac{3}{4}$
   4. $\frac{1}{2}$
2. What is $\frac{5}{6} - \frac{1}{3}$?
   1. $\frac{4}{3}$
   2. $\frac{1}{2}$
   3. $\frac{4}{9}$
   4. $\frac{2}{3}$
3. What is $\frac{2}{5} \times \frac{3}{4}$?
   1. $\frac{5}{9}$
   2. $\frac{6}{20}$
   3. $\frac{1}{2}$
   4. $\frac{3}{10}$
4. What is $\frac{1}{2} \div \frac{3}{4}$?
   1. $\frac{2}{3}$
   2. $\frac{3}{8}$
   3. $\frac{4}{6}$
   4. $\frac{1}{2}$
5. What is $-\frac{2}{3} + \frac{1}{6}$?
   1. $-\frac{1}{2}$
   2. $\frac{1}{2}$
   3. $-\frac{3}{9}$
   4. $-\frac{1}{3}$
6. What is $-\frac{1}{4} - \frac{1}{2}$?
   1. $-\frac{2}{6}$
   2. $-\frac{3}{4}$
   3. $\frac{1}{4}$
   4. $\frac{3}{4}$
7. What is $-\frac{3}{5} \times -\frac{2}{7}$?
   1. $-\frac{6}{35}$
   2. $\frac{5}{12}$
   3. $\frac{6}{35}$
   4. $-\frac{5}{12}$