Add fractions with unlike denominators
To add fractions with different denominators, you need to find a 'common denominator'. Think of it as finding a common language so the fractions can work together. Once they have a common denominator, adding is easy!
Concept
You can't add fractions with different denominators directly because the pieces are different sizes. You must first convert them into equivalent fractions with a shared, or "common," denominator. **The Steps to Success:** 1. **Find the Least Common Denominator (LCD):** The LCD is the smallest number that both denominators can divide into. This is also called the Least Common Multiple (LCM) of the denominators. 2. **Create Equivalent Fractions:** Rewrite each fraction as an equivalent fraction with the new LCD. 3. **Add the Numerators:** Now that the denominators are the same, simply add the numerators. 4. **Simplify:** If possible, simplify the resulting fraction to its lowest terms. **Example: 1/3 + 1/4** 1. **Find the LCD:** * Multiples of 3: 3, 6, 9, **12**, 15... * Multiples of 4: 4, 8, **12**, 16... * The LCD is **12**. 2. **Create Equivalent Fractions:** * For 1/3: How do you get from 3 to 12? Multiply by 4. So, do the same to the numerator: 1 x 4 = 4. The new fraction is **4/12**. * For 1/4: How do you get from 4 to 12? Multiply by 3. So, do the same to the numerator: 1 x 3 = 3. The new fraction is **3/12**. 3. **Add the Numerators:** * 4/12 + 3/12 = **7/12** 4. **Simplify:** * 7/12 is already in its simplest form. **Visual Model:** Imagine one pizza cut into thirds and another cut into fourths. You can't easily combine the slices. But if you slice both pizzas into twelfths, you can see that 1/3 is the same as 4/12 and 1/4 is the same as 3/12. Now you can easily add the slices: 4 + 3 = 7 twelfths. **Key Idea:** The goal is to make the pieces the same size (by finding a common denominator) before you try to count them together.
Try it
Practice adding fractions! **Find the LCD:** 1. What is the LCD for 1/2 and 1/5? 2. What is the LCD for 2/3 and 5/6? 3. What is the LCD for 1/4 and 1/5? **Solve the problems:** 4. 1/2 + 1/4 = ? 5. 2/3 + 1/6 = ? 6. 1/5 + 1/2 = ? 7. 3/4 + 1/8 = ? 8. 2/3 + 1/5 = ? **Word Problems:** 9. You ate 1/3 of a pizza and your friend ate 1/2 of it. How much of the pizza did you eat combined? 10. A recipe calls for 1/2 cup of white sugar and 1/4 cup of brown sugar. What is the total amount of sugar? 11. You walk 3/4 of a mile to the store and then another 1/3 of a mile to the park. How far did you walk in total? **Challenge Problems:** 12. 1/2 + 1/3 + 1/4 = ? (Hint: Find a common denominator for all three!) 13. What is 5/6 + 3/8? Make sure to simplify your answer.