Lesson 5-7

Example 1	Add Unlike Fractions
Find  + .
 +  =    +   		Use 4  5 or 20 as the common denominator.
=  +           	Rename each fraction with the common denominator.	
=                     	Add the numerators.

Example 2	Add Fractions and Mixed Numbers
Find each sum.  Write in simplest form.
a.   +		Estimate:  - = 0
 +  =    +   	The LCD of 12 and 8 is 24.
	=  + 		Rename each fraction with the LCD.
	= 			Add.  Compare to the estimate.  Is the answer
reasonable?

b.  2 + 		Estimate:  3 - 1 = 2
2 +  =  + 		Write the mixed numbers as improper fractions.
	=    +  	Rename  and  using the LCD, 12.
	=  + 		Simplify.
	=  or .		Add.  Compared to the estimate, the answer is 
reasonable. 

Example 3	Subtract Fractions and Mixed Numbers
Find each difference.  Write in simplest form.
a.   - 
  - 	=    - 		The LCD is 18.
	=  - 		Rename using the LCD.
	= -			Subtract.

b.  5 - 2
  5 - 2	=  - 		Write as improper fractions.
	=  -   		Rename using the LCD.
	=  - 		Simplify.
	=  or 2		Subtract.

Real-World EXAMPLE
Example 4	Use Fractions to Solve a Problem
HIKING	Peter hiked a total of 2miles.  If he hiked 1 miles east,  mile south, how many miles did he hike west?

Explore	You know distance of the total hike, 2miles, and the distance of two
sections of the hike, 1 and .

Plan	Add the known distances and subtract that sum from 2.  
Estimate your answer.
	3 – (2 + 1) = 0
Solve		1 +   = 1 + 		Rename fractions with the LCD, 8.
			    = 1 or    	Simplify.
		2-  = or  		Subtract and simplify.
		Peter hiked miles west.		
Check		Since  is close to 0, the answer is reasonable.