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!
Do this: Read the concept below, then try the quiz or activity.
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 = 7/124. 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.