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**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 ( , ) R: Real (all rational and irrational)

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Real Numbers, R IMAGINARY I Q Z W N

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**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 in note zero, then

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**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

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**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

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**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

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**Applications of Equations**

Problem Solving Plan Explore the Problem Plan the solution Solve the problem Examine the solution

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**Absolute Value Equations**

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

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