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# Math115, Chapter P Textbook Notes MATH 115

Towson

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This 2 page Class Notes was uploaded by Stacy Downing on Saturday January 30, 2016. The Class Notes belongs to MATH 115 at Towson University taught by Ellen M. Johnson in Fall 2015. Since its upload, it has received 11 views. For similar materials see Basic Math for The Sciences in Mathmatics at Towson University.

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Date Created: 01/30/16

Math 115 Textbook Notes: Chapter P the Fundamental Concepts of Algebra 1 Exponential Notation: b = b · b · b ·… ·b (Factors of n) Set: {1, 2, 3, 4, 5,} Union of Set: A U B = A or B Intersection of Set: A Ƞ B = A and B Subsets of the Real Numbers Name Description Examples Natural The # that we use for counting 2, 3, 5, 17 # Whole # Whole #’s that includes 0 and natural # 0, 2, 3, 5, 17 Integers Includes the negatives of the natural # and whole # -17, -5, -3, -2, 0, 2, 3, 5, 17 Rational All #s that can be expressed as a quotient of two -17=-17/1, 5= 5/1, 2/5=0.4, # integers -3, 2, 0 Irrational All # whose decimals are neither termination nor √2=1.414214,− 3√ = # repeating -1.73205 Real Numbers # that are either rational or irrational Symbo Meaning Example Explanation ls a ≤ b a is less than or equal to b 2 ≤ 9 Because 2 < 9 9 ≤ 9 Because 9 = 9 a ≥ b a is greater than or equal to b 9 ≥ 2 Because 9 > 2 2 ≥ 2 Because 2 = 2 Absolute Value distance from 0 to a The Product Rule b · b = b m+n The Quotient Rule b /b = b m-, b≠ 0 0 The Zero Exponent Rule b = 1 The Negative Exponent Rule b = 1/b n The Power Rule (b ) = b mn n n n Products to Power (ab) = a b Quotient to Power (a/b) = a /b n 2 2 Simplifying √a = │ a │ (e.g. √ −6 ) = │-6│= 6 The Product Rule for Square Roots √ ab= √ √b∧ a√ √= ab √ √a The Quotient Rule for Square Roots b= √/b √ n √a = a,n odd Nth roots of perfect nth powers {a|,∧neven n n The Principal nth Root of a Real Number √a=bmeansb =a n a 1/= √a 1 a -1=n n √ a n a m/n =√a m F. O. I. L. (ax + b)(cx + d) = ax · cx + ax · d + b· cx + b · d (A + B)(A - B)= A – B 2 2 2 2 (A + B) = A + 2AB + B (A - B) = A – 2AB + B 2 (A + B) = A + 3A B + 3AB + B 2 3 3 3 2 2 3 (A-B) = A – 3A B + 3AB – B S. O. A. P. = Same Sign Opposite Sign Always Plus 3 3 2 2 o A + B = (A + B)(A - AB + B ) o A – B = (A – B)(A + AB + B ) 2 Least Common Denominator o Step 1: Factor out to the point where it is fully simplified o Step 2: List factors of the first denominator o Step 3: List the factors of both o Determine the LCD by multiplying all the factors in Step 3 together Simplifying a Complex Rational Expression o Step 1: Add to get a single rational expression in the numerator o Step 2: Subtract to get a single rational exponent in the denominator o Step 3: Perform the division

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