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Learn basic algebra, real number system, and operations with real numbers in MM201 Unit 1 Seminar. Engage with discussions and complete assignments. Join today!
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MM201 Unit 1 Seminar Agenda • Welcome and Syllabus Review • A Review of Basic Algebra • The Real Number System • Operations with Real Numbers
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Weekly Assignments • CNOW quiz 20 points – ENTER ONE TIME! • CNOW project 30 points – can work on it through the week • Word Project – 30 points – the power assignment! • Seminar – 6 points - come or take quiz • Discussion Board – 10 points
How do you see your CNOW results? Go to view all assignments in CNOW - then under actions select view. You will be able to view an assignment after the deadline has passed.
Discussion Board Expectations • Two threads: 5 points each • Thread 1: Post a problem NOT already worked by a classmate • Show your work in detail. • State which problem you are working as your first line • Correct grammer and spelling required • Thread 2: Answer the question posted and provide a mathematical example. • Correct grammer and spelling required • Read my expectations in doc-sharing • What you can GET from the discussions…
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Examples • Variables: x, y, z, a • Algebraic Expression: • a + b • 4x – 7 • 6y • x/4 • They can be longer, like these:3x2 – 7y3 + 12z – 2 • a + b + c + d + e + f + g
Sets of Numbers • Natural Numbers: 1, 2, 3, 4, … • Whole Numbers: 0, 1, 2,3, … • Integers: …-3, -2, -1, 0, 1, 2, 3, … • Rational Numbers: ½, 0.5, -6, • Irrational Numbers: , √[2], √[3] • Real Numbers: all rational and irrational numbers
Operations with Real Numbers • Additive Inverse means opposite The additive inverse of-10x is 10x • Absolute Value is the distance from zero • Sign Rules for Addition/Subtraction Same sign: add and take that sign -5 + -5 = -10 Different sign: subtract and take the sign of the larger -10 + 5 = -5 [if subtracting, change the – to + (-)]: -5 - 2 = -5 + (-2) = -7 • Sign Rules for Multiplication/Division Same sign: positive Different sign: negative • “0” in Division: 0 in numerator is 0 0 in denominator is undefined
Exponents: x^2 is the same as x2 2^3 = 23 = 2*2*2 = 8 Be careful! (-2)4 = (-2)(-2)(-2)(-2) = 16 -24 = -2*2*2*2 = -16 • Square roots: √[36] = 6 • Order of Operations Mneumonic Device: Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) **Note be careful because multiplication and division are together, and addition and subtraction are together. 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5 in parentheses, 3 – 5 = -2 = 2(4) + 5 in parentheses, -2 + 6 = 4 = 8 + 5 got rid of parentheses by multiplying 2*4 = 8 = 13 addition is all that’s left: 8 + 5 = 13
Evaluating Expressions is like substitution Evaluate x + 4 for x = 3 Replace x with 3, then follow the order of operations to simplify. x + 4 = 3 + 4 = 7 • Perimeter is the distance around a closed figure Example: The sides of a triangle have lengths of 3 meters, 7 meters, and 4 meters. Determine the perimeter. Add all the side lengths together. 3 + 7 + 4 = 14 Therefore, the perimeter is 14 meters • Area is the measurement of surface measured in square units Example: Find the area of a rectangular yard enclosed by a fence 12 yards long and 8 yards wide. The area of a rectangle can be found using this formula: A = LW A = (12)(8) A = 96 Therefore, the area is 96 square yards. • Volume is space within a figure measured in cubed units The volume of a cubic shape can be found using this formula: V = LWH V = (10)(6)(4) V = 240 Therefore, the volume is 240 cubic feet. • Right Angles measure 90° • Altitude is a line PERPENDICULAR (at a right angle) to the base (the flat side of the object, considered to be the bottom of the object).