Add and Subtract Fractions with Unlike Denominators
You can't add apples and oranges... or can you? When fractions have different denominators, you need to find a common language first! Let's learn how to make fractions compatible so we can add and subtract them.
Concept
To add or subtract fractions with different denominators, you must first find a common denominator! šÆ **The Main Rule:** Fractions need the SAME denominator to be added or subtracted! š **Why We Need Common Denominators:** Think of it like money: ā¢ Can you add 2 quarters + 3 dimes directly? No! ā¢ You need to convert to the same unit (cents): 50Ā¢ + 30Ā¢ = 80Ā¢ ā¢ Same with fractions! š” **The Process:** **Example: 1/4 + 1/6** **Step 1: Find a common denominator** Multiples of 4: 4, 8, 12, 16, 20... Multiples of 6: 6, 12, 18, 24... Common denominator: 12 (LCM) **Step 2: Convert both fractions** ā¢ 1/4 = ?/12 ā (1 Ć 3)/(4 Ć 3) = 3/12 ā¢ 1/6 = ?/12 ā (1 Ć 2)/(6 Ć 2) = 2/12 **Step 3: Add the numerators** 3/12 + 2/12 = 5/12 **Step 4: Simplify if needed** 5/12 is already in simplest form! š **Subtraction Works the Same Way:** **Example: 5/6 - 1/4** **Step 1:** Common denominator = 12 **Step 2:** Convert: 5/6 = 10/12 and 1/4 = 3/12 **Step 3:** Subtract: 10/12 - 3/12 = 7/12 **Step 4:** Already simplified! šØ **Finding Common Denominators:** **Method 1: List multiples** For 3 and 4: ā¢ Multiples of 3: 3, 6, 9, 12... ā¢ Multiples of 4: 4, 8, 12... ā¢ LCD = 12 **Method 2: Multiply denominators** (Quick but not always smallest!) ā¢ 1/3 + 1/5 ā use 3 Ć 5 = 15 as common denominator ā¢ 1/3 = 5/15 and 1/5 = 3/15 ā¢ 5/15 + 3/15 = 8/15 š **Visual Model:** Draw fraction bars! 1/2 + 1/3: [ā®ā®|ā®ā®|ā®ā®] = 3/6 (1/2) [ā®ā®|ā®ā®] = 2/6 (1/3) Together: 5/6 **Key Reminder:** Only the denominators must match - the numerators can be different!
Try it
Practice adding and subtracting fractions with unlike denominators! š **Find Common Denominators:** 1. What's a common denominator for 1/2 and 1/3? 2. What's the LCD (least common denominator) for 1/4 and 1/6? 3. What's a common denominator for 2/5 and 1/10? šÆ **Add These Fractions:** 4. 1/2 + 1/4 = ? (Hint: Common denominator is 4) 5. 1/3 + 1/6 = ? 6. 2/5 + 1/2 = ? 7. 1/4 + 1/3 = ? š” **Subtract These Fractions:** 8. 3/4 - 1/2 = ? 9. 5/6 - 1/3 = ? 10. 4/5 - 1/2 = ? 11. 7/8 - 1/4 = ? š **Mixed Practice:** 12. 2/3 + 1/4 = ? 13. 5/6 - 2/9 = ? 14. 3/10 + 1/2 = ? 15. 3/4 - 1/6 = ? š **Word Problems:** 16. Sarah ate 1/3 of a pizza. Her brother ate 1/4 of the same pizza. What fraction of the pizza did they eat together? 17. Marcus had 3/4 of a gallon of paint. He used 1/3 of a gallon. How much paint does he have left? 18. A recipe calls for 1/2 cup of flour and 1/3 cup of sugar. How many cups of dry ingredients total? šŖ **Challenge:** 19. 2/3 + 1/4 + 1/6 = ? (Hint: Find common denominator for all three!) 20. If you walk 3/4 mile to school and 2/3 mile to the park, how much farther did you walk to school? 21. Simplify your answer: 5/6 + 3/8 = ?