1. M3U5D4b Warmup Subtract. Write in simplest terms:

2. Homework Check:
None

3. M3U5D4b Complex Fractions
OBJ: Add, subtract, multiply, and divide rational expressions. (A-APR.7)

4. Complex Fractions.
The quotient of two mixed numbers in arithmetic, such as can be written as a fraction.
The last expression is the quotient of expressions that involve fractions. In algebra, some rational expressions also have fractions in the numerator, or denominator, or both.
A rational expression with one or more fractions in the numerator, or denominator, or both is called a complex fraction.
The parts of a complex fraction are named as follows.
Numerator of complex fraction
Main fraction bar
Denominator of complex fraction

5. Simplify a complex fraction by writing it as a division problem
Method 1
Simplify a complex fraction by writing it as a division problem

6. Simplify a complex fraction by writing it as a division problem (Method 1).
Since the main fraction bar represents division in a complex fraction, one method of simplifying a complex fraction involves division.
Step 1: Write both the numerator and denominator as single fractions.
Step 2: Change the complex fraction to a division problem.
Step 3: Perform the indicated division.

7. EXAMPLE 1 Simplify each complex fraction. Solution:
Simplifying Complex Fractions (Method 1)
Simplify each complex fraction.
Solution:

8. EXAMPLE 2 Simplify the complex fraction. Solution:
Simplifying a Complex Fraction (Method 1)
Simplify the complex fraction.
Solution:

9. EXAMPLE 3 Simplify the complex fraction. Solution:
Simplifying a Complex Fraction (Method 1)
Simplify the complex fraction.
Solution:

10. Method 2
Simplify a complex fraction by multiplying by the least common denominator.

11. Simplify a complex fraction by multiplying the least common denominator (Method 2).
Since any expression can be multiplied by a form of 1 to get an equivalent expression, we can multiply both the numerator and denominator of a complex fraction by the same nonzero expression to get an equivalent rational expression. If we choose the expression to be the LCD of all the fractions within the complex fraction, the complex fraction will be simplified.
Step 1: Find the LCD of all fractions within the complex fraction.
Step 2: Multiply both the numerator and denominator of the complex fraction by this LCD using the distributive property as necessary. Write in lowest terms.

12. EXAMPLE 4 Simplify each complex fraction. Solution:
Simplifying Complex Fractions (Method 2)
Simplify each complex fraction.
Solution:

13. EXAMPLE 5 Simplify the complex fraction. Solution:
Simplifying a Complex Fraction (Method 2)
Simplify the complex fraction.
Solution:

14. EXAMPLE 6 Simplify each complex fraction.
Deciding on a Method and Simplifying Complex Fractions
Simplify each complex fraction.
Remember the same answer is obtained regardless of whether Method 1 or Method 2 is used. Some students prefer one method over the other.

15. Check together using document camera
Classwork
M3U5D4 Complex Fractions
#1-5
Check together using document camera

16. Classwork examples from Smartboard:

17. Classwork examples from Smartboard:

18. Homework
M3U5D4 Complex Fractions #7, 10, 12, 14 Return Test … Corrections due Monday 12/4/17 Retest Tues 12/5 or Wed 12/6