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Lesson 1 Using properties of real numbers

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A set is a collection of objects If all the members of one set are also members of a second set, then the first set is a subset of the second.

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Real numbers are a set of numbers consisting of several subsets of numbers Real numbers consist of rational numbers (can be written as a quotient of integers) and irrational numbers Rational numbers include the natural numbers-1,2,3,4,…, the whole numbers- 0,1,2,3,….. and the integers-….-3,-2,-1,0,1,2,3…

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Identifying subsets of numbers Identify the subsets of which each number is a member: -16 32 3/4 Pi Square root of 2 -(square root of 20)

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Properties of addition and multiplication If a,b,c are real numbers Property addition multiplication 1)Closure a +b is real # ab is real # 2)commutative a+b=b+a ab = ba 3)associative (a+b)+c=a+(b+c) (ab)c=a(bc) 4)distributive a(b+c)= ab +ac

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Identifying properties of real numbers Which property is demonstrated: 23+10=10+23 3x8=8x3 -3(7(-5))=(-3(7))(-5) 5(7+11)=5(7)+5(11) (12+30)+20= 12+(30+20)

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Simplify and identify each property used 12+4+18+56 12+ 18 +4 +56 (12+18) + (4+ 56) 30 + 60 90

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Identify the property used in each step 5(23) 5(20+3) (5x20) +(5x3) 100 + 15 115

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More properties of addition and multiplication Property addition multiplication Identity a+0=a,0+a=a a x1=a,1 x a=a Inverse a+(-a)= 0 a x 1/a = 1, a cannot be 0

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Finding inverses Find the additive inverse of 3a Find the multiplicative inverse of 2/y-5 Find the additive inverse of 3-d Find the multiplicative inverse of 5n/12p

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Lesson 2 evaluating expressions and combining like terms An algebraic expression can contain variables (letters that represent unspecified numbers) When you replace the variables in an expression with selected numbers and simplify using the order of operations, you have evaluated the expression

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Order of operations 1. parentheses and grouping symbols 2. exponents 3. Multiply and divide from left to right 4. add and subtract from left to right PEMDAS

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Evaluating expressions If a= -2 and b=4 Find a(-b-a)-ab If a = 5and b= -3 Find ab 2 -(a-b) and a 2 b +3 -2

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Practice with calculator (be careful- use parentheses with negative numbers) Evaluate 3mp +2p 2 if m = 6 and p =-3 Evaluate 5p 2 (6m+p) if m = 4 and p=-2 Evaluate m 2 p 2 -(m-p) if m= 4 and p=-2

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terms The terms of an algebraic expression are separated by addition and subtraction symbols LIKE TERMS have the same variables raised to the same power. (the order of the variables does not matter) Constant terms are always like terms. Add like terms by adding the coefficients of the terms

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Simplifying expressions 3xy - 2x + 4 -6yx + 3x 7mp + 8 -2m + 5pm -3

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Questions for understanding Explain the difference between (-x) 2 and -x 2 What is wrong with this and what should the answer be? 3x 2 + x + 4x = 8x 4 What is the difference between a set and a subset? Can a number be both rational and irrational? Explain.

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