Rational Number Operations
Rational numbers include fractions, decimals, and integers - any number that can be written as a fraction! Master adding and subtracting these numbers to handle real-world problems involving measurements, money, and more.
Concept
Rational numbers follow the same rules as integers, but with fractions and decimals! **WHAT ARE RATIONAL NUMBERS?** A rational number can be written as a fraction p/q where: - p and q are integers - q ≠ 0 Examples of rational numbers: - Integers: 5 = 5/1, -3 = -3/1 - Fractions: 2/3, -5/8, 7/4 - Decimals: 0.5 = 1/2, -2.75 = -11/4, 0.333... = 1/3 **ADDING AND SUBTRACTING FRACTIONS:** **Same Denominator:** Simply add/subtract the numerators, keep the denominator! Examples: - 3/7 + 2/7 = 5/7 - -5/9 + 2/9 = -3/9 = -1/3 - 4/5 - 7/5 = -3/5 **Different Denominators:** 1. Find the LCD (Least Common Denominator) 2. Convert to equivalent fractions 3. Add/subtract numerators 4. Simplify if needed Example: 1/3 + 1/4 - LCD = 12 - 1/3 = 4/12, 1/4 = 3/12 - 4/12 + 3/12 = 7/12 **With Negative Fractions:** Apply integer rules! Example: -2/5 + 3/5 = 1/5 (different signs → subtract, take larger sign) Example: -1/6 - 2/6 = -3/6 = -1/2 (same signs → add, keep sign) **ADDING AND SUBTRACTING DECIMALS:** **Line up decimal points!** Example: 3.75 + (-2.3) 3.75 + (-2.30) ← Add trailing zero for clarity ---------- 1.45 Example: -5.6 - 3.8 Think: -5.6 + (-3.8) = -9.4 (same signs, add, keep negative) **MIXED NUMBERS:** Convert to improper fractions OR work with whole and fraction parts separately Example: 2 1/4 + 1 3/4 Method 1: 9/4 + 7/4 = 16/4 = 4 Method 2: (2 + 1) + (1/4 + 3/4) = 3 + 4/4 = 3 + 1 = 4 **KEY STRATEGIES:** 1. **For Fractions:** Find common denominators 2. **For Decimals:** Line up decimal points 3. **For Mixed:** Convert or separate 4. **For Negatives:** Use integer addition/subtraction rules 5. **Always Simplify:** Reduce fractions, clean up decimals **REAL-WORLD APPLICATIONS:** - Cooking: Adding 1/2 cup + 3/4 cup of flour - Finance: Stock prices: $45.75 + (-$2.30) = $43.45 - Measurements: 3.5 meters - 1.8 meters = 1.7 meters - Temperature: -4.5°C + 7.2°C = 2.7°C
Try it
Build your rational number operation skills! **FRACTION ADDITION (Same Denominator):** 1. 5/12 + 7/12 = ? 2. -3/8 + 5/8 = ? 3. 2/9 + (-7/9) = ? **FRACTION ADDITION (Different Denominators):** 4. 1/3 + 1/6 = ? 5. 2/5 + 3/10 = ? 6. -1/4 + 2/3 = ? **FRACTION SUBTRACTION:** 7. 7/8 - 3/8 = ? 8. 5/6 - 2/3 = ? 9. -2/5 - 1/5 = ? 10. 3/4 - (-1/4) = ? **DECIMAL ADDITION:** 11. 5.6 + 3.9 = ? 12. -8.2 + 5.7 = ? 13. 12.45 + (-7.8) = ? **DECIMAL SUBTRACTION:** 14. 9.5 - 3.8 = ? 15. -6.3 - 2.9 = ? 16. 4.2 - (-3.5) = ? **MIXED NUMBERS:** 17. 2 1/2 + 3 3/4 = ? 18. 5 2/3 - 2 1/6 = ? **WORD PROBLEMS:** 19. A stock price decreased by $3.75 on Monday and increased by $2.50 on Tuesday. What was the total change? 20. A recipe calls for 2/3 cup of milk, but you want to make 1 1/2 times the recipe. How much milk do you need? 21. The temperature at 6 AM was -3.5°F. By noon it had risen 8.7°F. What was the noon temperature? **CHALLENGE:** 22. Evaluate: 1/2 - 3/4 + 5/8 - 1/8 (Find the LCD first!) 23. Simplify: -5.6 + 3.2 - (-4.8) + (-2.1)