Algebra 3.4 Algebra Properties mbhaub@mpsaz.org. February 11, 2014Geometry 2.4 Reasoning with...

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Transcript of Algebra 3.4 Algebra Properties mbhaub@mpsaz.org. February 11, 2014Geometry 2.4 Reasoning with...

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Algebra 3.4 Algebra Properties mbhaub@mpsaz.org Slide 2 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties2 Goals Use properties from algebra. Use properties to justify statements. Slide 3 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties3 Algebra Properties Dont copy all of this down You have had most before. Copy the ones that are new to you You need to have them all memorized. This as well as all presentations are available on-line. Slide 4 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties4 Addition Property If a = b, then a + c = b + c. Example x 12 = 15 x 12 + 12 = 15 + 12 x = 27 Slide 5 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties5 Subtraction Property Subtraction Property If a = b, then a c = b c Example x + 30 = 45 x + 30 30 = 45 30 x = 15 Slide 6 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties6 Multiplication Property If a = b, then ac = bc Example Slide 7 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties7 Division Property Example Slide 8 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties8 Other Properties Reflexive PropertyFor any number a, a = a. Symmetric PropertyIf a = b, then b = a. Transitive PropertyIf a = b and b = c, then a = c Substitution PropertyIf a = b and a = c, then b = c Distributive Property a(b + c) = ab + ac Slide 9 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties9 Identify the Property If 43 = x, then x = 43. Property? Symmetric Slide 10 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties10 Identify the Property If 3x = 12, then 12x = 48 Property? Multiplication Slide 11 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties11 Identify the Property If x = y, and y = 10, then x = 10 Property? Transitive Slide 12 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties12 Identify the Property If x = 12, then x + 2 = 14 Property? Addition Slide 13 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties13 Using a Property Addition Property: If n = 14, then n + 2 = _________ 16 Slide 14 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties14 Using a Property Symmetric: If AB = CD, then CD = ________ AB Slide 15 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties15 Using a Property Transitive: If m A = m B, and m B = m C, then m A = _________. m C Slide 16 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties16 Justification One of the main reasons to study Algebra is to learn how to prove things. The whole business of math is proving things. To prove things in math you must be able to justify everything with legitimate reasons. Our reasons include: postulates, definitions and algebra properties. Slide 17 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties17 Example Solve 3x + 12 = 8x 18 and write a reason for each step. 3x + 12 = 8x 18Given 5x = 30 Subtraction Property x = 6 Division Property 3x 8x + 12 12 = 8x 8x 18 12 Simplify (combine like terms) 5x/(5) = 30/(5) Simplify Slide 18 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties18 Another Example (w/o intermediate steps) Solve x+2(x 3) = 5x + 2 x + 2(x 3) = 5x + 2 x + 2x 6 = 5x + 2 3x 6 = 5x + 2 3x = 5x + 8 2x = 8 x = 4 Given Distributive Prop. Simplify Addition Prop. Subtraction Prop. Division Prop. Slide 19 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties19 Before we do a proof Any algebra proof must begin with information that we know is true. This will be given to us as a place to start, so it is called the given. There can be one or more givens in a problem. Slide 20 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties20 This is Proof. If you feel uncomfortable and confused, thats normal. Everyone is confused with proof at first. There is only one way to learn proof: PRACTICE. You have to know the properties, postulates and definitions. You must diligently practice by doing the homework every night NO EXCUSES. You learn by making mistakes. Everyone does. Slide 21 February 11, 2014Geometry 2.4 Reasoning with Algebra Properties21 Proof is essential. Proof is a mandatory part of higher math. If you plan on going to college and/or taking more advanced math you must prove things. Algebra is the place to learn to do this. We will do proofs until the end of the year. Dont fight it, they are not going to go away.