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.
Do this: Read the concept below, then try the quiz or activity.
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)