Elementary arithmetic

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Mathematical notation

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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Abstract algebra

Elementary mathematics

Mathematical notation

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)

1.1 Sets of Numbers

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Arithmetic

Elementary mathematics

Field theory

Real numbers

Number

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How to add fractions easilly

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Trigonometry

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Numbers

CNote

Pi

My Pre-Cal teacher taught us this. When you are trying to add fractions during a sine or cosine problem, or something that has to do with a unit circle or a triangle, use this: Ex: 1/4 + 3/5 Multiply 5*1, multiply 4*3 and add them for the numberator, and multiply 4*5 for the denominator. So it would be 5+12/20. 17/20. You multiply the denominator of one and numerator of other by the denominator of other and numerator of one.Then add. That will give you the numerator. Then the denomnator you multiply both denominators and add.

Basic Algebraic Formulas

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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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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)

Add+Subtract Rational Expressions

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Homework ???????????????Grade?8 Name:?___________________________________________ Date:?__________ The?LCM?of?two?rational?algebraic?expressions?is?often?used?to?add?or?subtract?the?two? expressions.?The?method?used?is?to?identify?all?common?factors?in?the?denominator?of? the?expressions,?and?multiply?the?numerators?by?the?uncommon?factors?(exactly?like?you? would?for?non?algebraic?fractions).? Add?or?subtract?the?following?expressions,?by?first?finding?the?LCD. 1. ????a???+????????a?+?x??????+???ax????? ???????????x???a?????x2?+?ax?+?a2??????x3???a3 2. ??1?????+??????5?????+???? ??x? ??????? ?? ???????????x?+?1????4x?+?4????x2???1 ?? 3. ????1?????+?????2x??????+???3x????+????x??????? ??????????3x???3??????(x???1)2???x?+?1?????(x?+?1)2?

Limits to infinity

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Calculus

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Philosophy of mathematics

Division

Numbers

CNote

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Limits

If a limit is approaching infinity, the highest exponent on the numerator or denominator determines whether its zero, or infinity

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Algebra Help

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Square

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Applying the Fundamental Concepts of Algebra An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. For engineers and scientists it is an essential requirement. The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here. USING REAL NUMBERS

properties of equations

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