2 IMPORTANT DEFINITIONS
term_{definition}: any "math expression" that is added or subtracted.
ex. 1) 5 + 4  6; 5 is a term and 4 is a factor and 6 is a term.
ex. 2) 2x + 5; 2x is a term and 5 is a term.
ex. 3) 3xy  7x + 4y + 10 ; 3xy is a term and 7x is a term and 4y is a term and 10 is a term..
factor_{definition}: any "math expression" that is multiplied.
ex. 1) (5)(4) ; 5 is a factor and 4 is a factor.
ex. 2) 5(x + 3) ; 5 is a factor and (x + 3) is a factor.
ex. 3) (3x  7)(x + 3) ; (3x  6) is a factor and (x + 3) is a factor.
SECTION 19.1: WHAT IS A
RATIONAL EXPRESSION?
A "rational expression" is a fraction with variables in the
numerator and/or the denominator and the variables have positive integer powers. See the examples below.
SECTION 19.2: ADDING AND
SUBTRACTING RATIONAL EXPRESSIONS
I am assuming that you know how to add, subtract, multiply, and divide
numerical fractions which are basic ideas of arithmetic. All the principles
you know about fractions in arithmetic apply to algebra.
ex. 1)
ex. 2)
ex.
1)
ex. 2)
SECTION 19.3: MULTIPLYING AND
DIVIDING RATIONAL EXPRESSIONS
ex. 1)
ex. 2)
ex. 3)
ex. 4)
A GENERAL COMMENT ON ADDING, SUBTRACTING,
MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS 
Make sure that the answer you give when adding, subtracting, multiplying and dividing is in "LOWEST TERMS." A fraction or rational expression is in lowest terms when the greatest common factor of the numerator and denominator is 1.

RULE OF CANCELLING 
When simplifying a rational expression(i.e. fraction) you can only cancel common factors. YOU CANNOT CANCEL LIKE TERMS!
Comment: common factors are also called "like factors." 
THE METHOD FOR REDUCING A RATIONAL
EXPRESSION TO LOWEST TERMS 
FACTOR THE NUMERATOR AND DENOMIANTOR, THEN CANCEL THE COMMON FACTORS IN THE NEMERATOR AND DENOMINATOR 


PLEASE NOTE THAT THE RULE OF CANCELING WAS IN CHAPTER 7. YOU MAY WANT
TO REVIEW THIS. 

IMPORTANT HINTS:

At times the G.C.F. of a numerator and denominator is not clear. Here are some
helpful hints:
RULE 1) When presented with all numbers in the numerator and
denominator, rewriting the numerator and denominator as a product of primes
is a quick way to determine what can cancel in the numerator and denominator.
RULE 2) When presented with polynomials in the numerator and
the denominator make sure to check to see if one and or the other can be
factored.



THE SUMMER STUDY GUIDE
BY CHAPTERS

RETURN TO THE SUMMER STUDY GUIDE MAIN PAGE
 CHAPTER 1: THE NUMBER SYSTEM
 CHAPTER 2: ORDER OF OPERATIONS
 CHAPTER 3: VARIABLES, MONOMIALS,
BINOMIALS, TRINOMIALS, POLYNOMIALS,
COEFFICIENTS, TERMS AND LIKE TERMS
 CHAPTER 4: SIGNED NUMBERS,
ABSOLUTE VALUE, AND INEQUALITY SYMBOLS
 CHAPTER 5: FACTORS, COMMON
FACTORS, LEAST COMMON FACTORS AND GREATEST COMMON FACTORS
 CHAPTER 6: PROPERTIES OF NUMBERS
 CHAPTER 7: THE WORLD OF FRACTIONS
 CHAPTER 8: EXPONENTS
 CHAPTER 9: ROOTS
 CHAPTER 10: ALGEBRAIC EXPRESSIONS
 CHAPTER 11: CARTESIAN COORDINATE SYSTEM
 CHAPTER 12: SETS, RELATIONS AND FUNCTIONS
 CHAPTER 13: AVERAGE RATE OF CHANGE OF Y WITH RESPECT TO X, SLOPE, PYTHAGOREAN THEOREM, AND DISTANCE FORMULA BETWEEN TWO POINTS
 CHAPTER 14: XINTERCEPT(ZERO) AND Y INTERCEPT(B)
 CHAPTER 15: LINES
 CHAPTER 16: FUNCTIONS
 CHAPTER 17: MULTIPLYING POLYNOMIALS
 CHAPTER 18: FACTORING
 CHAPTER 19: RATIONAL EXPRESSIONS
 CHAPTER 20: SOLVING EQUATIONS
 CHAPTER 21:SOLVING INEQUALITIES
 CHAPTER 22: SOLVING A SYSTEM OF EQUATIONS
 CHAPTER 23: QUADRATICS
 CHAPTER 24: CIRCLES
 CHAPTER 25: AREAS AND PERIMETERS OF PLANE FIGURES
 CHAPTER 26: VOLUMES
