1. Addition, Subtraction, and Complex Fractions
8.2
Addition, Subtraction, and Complex Fractions

2. Adding and Subtracting with Common Denominator

3. Example 1: Perform the indicated operation.

4. Adding and Subtracting with Unlike Denominators

5. Finding the LCD (LCM) Factor all denominators
The LCD contains each factor the greatest number of times it appears as a factor.

6. Example 2: Find the LCD.

7. Find the LCD.

8. Find the LCD.

9. Example 3: Add or Subtract.

10. Example 3: Add or Subtract.

11. Example 3: Add or Subtract.

12. Warm up Find the LCM: 1. 15a2bc3, 16b5c2, and 20a3c6
2. 4x2 – 1, x , and 2x + 1

13. Rational Models Example:
Josh drove 42 miles and then took the train. The entire trip was 172 miles. The average speed of the train was 35 mi/h faster than the average speed of the car. Let x equal the average speed of the car and y equal the total time traveled.
Then is the time the car traveled and is the time the train traveled.
What is the time Josh traveled in the car if his rate is 35 mi/h? What is his time on the train if his car rate is 35 mi/h?
Write a model that shows the total time it takes for the trip. If the average speed of the car was 50 mi/h, use your model to find how long did the trip will take?

14. Simplifying Complex Fractions.
Complex fraction: a fraction that contains a fraction in its numerator or denominator.

15. Example 5: Simplify.

16. Example 5: Simplify.

17. Example 5: Simplify.

18. Simplify