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Binary operations

Note Taking Guide 1.6

Subject: 
Algebra
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Mathematics
Binary operations
Elementary arithmetic
Mathematical notation
Elementary algebra
Algebra
Addition
Subtraction
Multiplication

1.06 Translations Essential Questions After completing this lesson, you will be able to answer these questions: How can translations help me understand how to represent verbal phrases as algebraic expressions? What are the key words and phrases that indicate certain operations? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Translation (Pg. 2) English to Algebra Addition Terms ? ___________ Subtraction Terms ? l__________ Multiplication Terms ? ___________ Division Terms ? ___________ EX: 4 times the difference of n and 8 ___________ EX: The area of a triangle is found by taking half of the product of the base times the height ___________ EX: x more than 5 ___________ EX: 9 subtracted from x ___________ EX: 25% of x ___________

Note Taking Guide 1.1

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Algebra
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Mathematics
Algebra
Abstract algebra
Elementary arithmetic
Binary operations
Elementary mathematics
Mathematical notation
Integers
Subtraction
Division
Multiplication
Number

Numerical Operations Essential Questions After completing this lesson, you will be able to answer the following questions: How are expressions rewritten in simplified form based on the mathematical operations in the expression? What is the correct order for performing mathematical operations in simplifying expressions? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Real Numbers(P.1) Natural Number: _______________ integers ____________ Numbers: A member of the set of positive integers or zero Integers: A number that can be written without a fraction or _______________ Rational Numbers: Can include positive/negative fractions and decimals. Irrational Number: Any real number that can not be expressed as a ratio. Adding and Subtracting Integers(P.2)

Logarithms

Subject: 
Calculus
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Fields of mathematics
Mathematics
Logarithms
Mathematical analysis
Binary operations
Additive function
Exponentials
Napierian logarithm
Common logarithm
Natural logarithm
John Napier
Exponentiation
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logarithms

Many students in high school and in college have a difficult time with logarithms. In many cases, they memorize the rules without fully understanding them, and they sometimes even manage to squeak by a course. Why waste their time on these archaic entities; they are never going to see them again. Wrong! Just when the student breathes a sigh of relief to be done with logarithms, they encounter them again in another course. They are now in trouble because the second encounter with logarithms is at a more sophisticated level. Without an understanding of the basics, the student is doomed to blindly stumble through and fail the course. You have our sympathy and you have our solution. We at S.O.S. Math want you to succeed.

Basic Algebraic Formulas

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Algebra
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Binary operations
Elementary arithmetic
Addition
Subtraction
Technology

Closure Property of Addition Sum (or difference) of 2 real numbers equals a real number Additive Identity a + 0 = a Additive Inverse a + (-a) = 0 Associative of Addition (a + b) + c = a + (b + c) Commutative of Addition a + b = b + a Definition of Subtraction a - b = a + (-b) Closure Property of Multiplication Product (or quotient if denominator 0) of 2 reals equals a real number Multiplicative Identity a * 1 = a Multiplicative Inverse a * (1/a) = 1 ? ? (a 0) (Multiplication times 0) a * 0 = 0 Associative of Multiplication (a * b) * c = a * (b * c) Commutative of Multiplication a * b = b * a Distributive Law a(b + c) = ab + ac Definition of Division a / b = a(1/b)

Formulas

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Algebra
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Binary operations
Elementary arithmetic
Mathematics
Closure
Addition
Subtraction

Closure Property of Addition Sum (or difference) of 2 real numbers equals a real number Additive Identity a + 0 = a Additive Inverse a + (-a) = 0 Associative of Addition (a + b) + c = a + (b + c) Commutative of Addition a + b = b + a Definition of Subtraction a - b = a + (-b) Closure Property of Multiplication Product (or quotient if denominator 0) of 2 reals equals a real number Multiplicative Identity a * 1 = a Multiplicative Inverse a * (1/a) = 1 ? ? (a 0) (Multiplication times 0) a * 0 = 0 Associative of Multiplication (a * b) * c = a * (b * c) Commutative of Multiplication a * b = b * a Distributive Law a(b + c) = ab + ac Definition of Division a / b = a(1/b)
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