🔢 Part 1: Adding Fractions with Different Denominators

1. Calculate: 1/3 + 1/4

Explanation: To add fractions with different denominators, first find the lowest common denominator (LCD). The LCD of 3 and 4 is 12. Convert both fractions: 1/3 = 4/12 and 1/4 = 3/12. Then add the numerators: 4/12 + 3/12 = 7/12

2. Calculate: 2/5 + 3/10

Explanation: The LCD of 5 and 10 is 10 (since 10 is a multiple of 5). Convert 2/5 to tenths: 2/5 = 4/10. Then add: 4/10 + 3/10 = 7/10

3. Calculate: 1/6 + 2/9

Explanation: Find the LCD of 6 and 9. List multiples: 6: 6, 12, 18... and 9: 9, 18... The LCD is 18. Convert: 1/6 = 3/18 and 2/9 = 4/18. Add: 3/18 + 4/18 = 7/18

➖ Part 2: Subtracting Fractions

4. Calculate: 3/4 - 1/3

Explanation: Find the LCD of 4 and 3, which is 12. Convert both fractions: 3/4 = 9/12 and 1/3 = 4/12. Subtract the numerators: 9/12 - 4/12 = 5/12

5. Calculate: 5/6 - 1/4

Explanation: The LCD of 6 and 4 is 12. Convert: 5/6 = 10/12 and 1/4 = 3/12. Subtract: 10/12 - 3/12 = 7/12

✖️ Part 3: Multiplying Fractions

6. Calculate: 2/3 × 3/5

Explanation: To multiply fractions, multiply the numerators together and the denominators together: (2 × 3)/(3 × 5) = 6/15. Simplify by dividing both numerator and denominator by their greatest common factor (3): 6/15 = 2/5

7. Calculate: 4/7 × 2/3

Explanation: Multiply across: (4 × 2)/(7 × 3) = 8/21. Check if this can be simplified - since 8 and 21 share no common factors, 8/21 is already in simplest form.

➗ Part 4: Dividing Fractions

8. Calculate: 1/2 ÷ 1/4

Explanation: To divide fractions, multiply by the reciprocal (flip the second fraction). So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. This means "how many quarters fit into a half?" - the answer is 2.

9. Calculate: 3/5 ÷ 2/3

Explanation: Multiply by the reciprocal: 3/5 × 3/2 = (3 × 3)/(5 × 2) = 9/10

🔄 Part 5: Converting Between Mixed Numbers and Improper Fractions

10. Convert 2 1/3 to an improper fraction

Explanation: Multiply the whole number by the denominator, then add the numerator: (2 × 3) + 1 = 7. Keep the same denominator: 7/3

11. Convert 17/5 to a mixed number

Explanation: Divide the numerator by the denominator: 17 ÷ 5 = 3 remainder 2. The quotient becomes the whole number, the remainder becomes the new numerator: 3 2/5

📊 Part 6: Real-World Fraction Problems

12. Sarah ate 1/4 of a pizza and Tom ate 1/3 of the same pizza. What fraction of the pizza did they eat altogether?

Explanation: Add the fractions: 1/4 + 1/3. Find LCD of 4 and 3, which is 12. Convert: 1/4 = 3/12 and 1/3 = 4/12. Add: 3/12 + 4/12 = 7/12 of the pizza.

13. A recipe calls for 3/4 cup of flour, but you want to make half the recipe. How much flour do you need?

Explanation: Calculate half of 3/4 by multiplying: 3/4 × 1/2 = 3/8 cup of flour

14. Which is larger: 2/3 or 5/8?

Explanation: Convert to the same denominator. LCD of 3 and 8 is 24. Convert: 2/3 = 16/24 and 5/8 = 15/24. Since 16/24 > 15/24, therefore 2/3 > 5/8