MATH 104q Intr Col Algebra&math Modeling UConn

UCONN - Math 1011Q Fraction Rules 1. Cancellation: ac a = bc b 2. Multiplication: a c ac = b d bd Remark: Any number a can be written as a fraction a = a . You can use this fact and the 1 multiplication rule to multiply any number by a fraction:

UCONN - Math 1011Q Radicals n and m denote positive integers ( nth Root: n a = b means b n = a If n is even then: n a is not defined for a < 0, and n a is positive for a > 0. If n is odd then: n a is always defined, and is uniquely determined by

UCONN - Math 1011Q Solving Linear Equations and Inequalities ( To Solve a Linear Equation do: 1. Clear the equation of fractions by multiplying both sides of the equal sign by the LCD. 2. Eliminate parentheses using the distributive law. 3. Combine

UCONN - Math 1011Q Roots and Factorization of Trinomials ( A trinomial (or quadratic) is an expression of the form ax2 + bx + c, where x is a variable and a, b and c are numbers, a 0. ( A root (or a solution) of a quadratic equation ax2 + bx + c =

UCONN - Math 1011Q The Conversion Rectangle Trick Use: To answer questions of percentages, or convert from one kind of units to another. Principle: Set up a rectangle where the top horizontal side represents the known conversion (or percentage), and

UCONN- Math 1011Q Exponential and Logarithmic Functions ( Exponential Function y = bx ( for 0 < b 1 fixed number) y = bx for b > 1 for b < 1 Equality of exponents : bx = bz is equivalent to x = z ( Logarithmic Functions y = logbx ( for 0 < b 1

UCONN - Math 1011Q Rules of Exponents 1. Zero Exponent: 2. Product Rule: a0 = 1 an am = an+m an = anm am a n = 1 an 3. Quotient Rule: 4. Negative Exponent: To move a number or a symbol from the numerator to the denominator (or from the denomin

Math 104Q Exponential and Logarithmic Functions Exponential Function y = bx ( for 0 < b y = bx 1 fixed number) for b > 1 for b < 1 Equality of exponents : bx = bz is equivalent to x = z Logarithmic Functions y = logbx ( for 0 < b y = logbx mean

Math 104Q Fraction Rules 1. Cancellation: ac a = bc b 2. Multiplication: a c ac = b d bd Remark: Any number a can be written as a fraction a = a . You can use this fact and the 1 multiplication rule to multiply any number by a fraction: a b c d