Properties of Real Numbers

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Presentation transcript:

Properties of Real Numbers N: Natural (1,2,3, …) W: Whole (0,1,2,3,…) Z: Integers (… -2,-1,0,1,2,…) Q: Rationals (m/n; m,n integers) I: Irrational ( , 3.45978) R: Real (all rational and irrational)

Real Numbers, R IMAGINARY I Q Z W N

Properties of Real Numbers For any real numbers a, b, and c Addition Multiplication Commutative Associative Identity a + 0 = a = 0 + a Inverse If a is not zero, then

Properties of Real Numbers Distributive property For all real numbers a, b, and c a(b+c) = ab + ac and (b+c)a = ba + ca

Solving Equations; 5 Properties of Equality Reflexive For any real number a, a=a Symmetric Property For all real numbers a and b, if a=b, then b=a Transitive Property For all reals, a, b, and c, if a=b and b=c, then a=c

Solving Equations; 5 Properties of Equality Addition and Subtraction For any reals a, b, and c, if a=b then a+c=b+c and a-c=b-c Multiplication and Division For any reals a, b, and c, if a=b then a*c=b*c, and, if c is not zero, a/c=b/c

Applications of Equations Problem Solving Plan Explore the Problem Plan the solution Solve the problem Examine the solution

Absolute Value Equations Absolute value: Distance from zero For any real number a: If , then

Practice Problems Page 15 Problems 4-16, 19-35