Slide 1:ALGEBRA Engr. Lizette Ivy G. Catadman Instructor / Lecturer LECTURE NOTES & PROBLEM SETS: PART 3


Slide 2:FRACTIONS CLASSIFICATIONS PROPER FRACTION THE NUMERATOR IS LESS THAN THE DENOMINATOR. ( N < D ) THE VALUE IS ALWAYS LESS THAN 1.


Slide 3:FRACTIONS CLASSIFICATIONS IMPROPER FRACTION THE NUMERATOR IS EQUAL TO OR GREATER THAN THE DENOMINATOR. ( N ≥ D ) THE VALUE IS EITHER EQUAL TO OR GREATER THAN 1.


Slide 4:FRACTIONS CLASSIFICATIONS MIXED NUMBER SUM OF A WHOLE NUMBER AND A PROPER FRACTION. MIXED EXPRESSION SUM OF A POLYNOMIAL (OR MONOMIAL) AND A FRACTION.


Slide 5:FRACTIONS CLASSIFICATIONS COMPLEX FRACTION A FRACTION WHICH HAS ONE OR MORE FRACTIONS IN ITS NUMERATOR OR DENOMINATOR OR IN BOTH.


Slide 6:FRACTIONS NOTE: EQUIVALENT FRACTIONS ARE FRACTIONS THAT HAVE THE SAME VALUE. IN ALGEBRA, AS IN ARITHMETIC, A FRACTION EQUIVALENT TO THE ORIGINAL/GIVEN IF: BOTH THE NUMERATOR AND DENOMINATOR ARE MULTIPLIED BY THE SAME NON-ZERO NUMBER. BOTH THE NUMERATOR AND DENOMINATOR ARE DIVIDED BY THE SAME NON-ZERO NUMBER.


Slide 7:FRACTIONS NOTE: TO REDUCE A FRACTION TO ITS LOWEST TERM/S FACTOR BOTH NUMERATOR AND DENOMINATOR COMPLETELY, AND DIVIDE THE NUMERATOR AND DENOMINATOR BY ALL FACTORS COMMON TO BOTH. (CANCEL FACTORS COMMON TO THE NUMERATOR AND DENOMINATOR.


Slide 8:OPERATIONS ON FRACTIONS CASE 1: TO ADD AND SUBTRACT LIKE FRACTIONS (THE SAME DENOMINATOR) ADDITION & SUBTRACTION ADD AND/OR SUBTRACT THEIR NUMERATORS, PLACE THEM OVER THE COMMON DENOMINATOR, AND REDUCE THE RESULTING FRACTION TO ITS LOWEST TERMS.


Slide 9:OPERATIONS ON FRACTIONS CASE 2: TO ADD AND SUBTRACT UNLIKE FRACTIONS (DIFFERENT DENOMINATORS) ADDITION & SUBTRACTION TAKE THE DIFFERENT DENOMINATORS TO OBTAIN THE LEAST COMMON DENOMINATOR (LCD) BY USING LCM. TAKING A DENOMINATOR AT A TIME, DIVIDE THE LCD BY EACH OF THE DENOMINATORS; AND THEN MULTIPLY THE RESULTING QUOTIENTS TO THE CORRESPONDING NUMERATORS.


Slide 10:OPERATIONS ON FRACTIONS CASE 2: TO ADD AND SUBTRACT UNLIKE FRACTIONS (DIFFERENT DENOMINATORS) ADDITION & SUBTRACTION (CONTINUED) COMBINE LIKE TERMS IN THE RESULTING NUMERATORS AND PLACE THE ANSWER OVER THE LCD. REDUCE THE RESULTING FRACTION TO ITS LOWEST TERMS.


Slide 11:OPERATIONS ON FRACTIONS CASE 2: TO ADD AND SUBTRACT UNLIKE FRACTIONS (DIFFERENT DENOMINATORS) ADDITION & SUBTRACTION


Slide 12:OPERATIONS ON FRACTIONS MULTIPLICATION FACTOR ALL THE NUMERATORS AND DENOMINATORS OF THE FRACTIONS. CANCEL OUT ALL FACTORS COMMON TO BOTH THE NUMERATOR AND DENOMINATOR. THE ANSWER IS THE PRODUCT OF ALL THE REMAINING FACTORS IN THE NUMERATOR AND DENOMINATOR.


Slide 13:OPERATIONS ON FRACTIONS DIVISION MULTIPLY THE DIVIDEND BY THE MULTIPLICATIVE INVERSE (RECIPROCAL) OF THE DIVISOR.


Slide 14:COMPLEX FRACTIONS TO SIMPLIFY COMPLEX FRACTIONS: SIMPLIFY THE NUMERATOR AND DENOMINATOR BY COMBINING THE FRACTIONS INTO A SINGLE FRACTION IN BOTH THE NUMERATOR AND DENOMINATOR. DIVIDE THE SIMPLIFIED NUMERATOR AND DENOMINATOR. EXPRESS THE RESULT IN ITS LOWEST TERMS.


Slide 15:COMPLEX FRACTIONS