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)

Q Z W N I Real Numbers, R IMAGINARYIMAGINARY

Properties of Real Numbers For any real numbers a, b, and c AdditionMultiplication Commutative Associative Identitya + 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 ReflexiveFor 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

Comparing 2 Real Numbers 1.Approximate Irrational Numbers & fractions as a decimal (Remember: a fraction is just division) 2.Determine the larger of two numbers and place the appropriate inequality between them

Comparing 2 Real Numbers Compare and 3.8 using or

Comparing 3 Real Numbers 1.Approximate Irrational Numbers & fractions as a decimal (Remember: a fraction is just division) 2.Rewrite them left to right in ascending order 3.Put a less than symbol (<) between them

Comparing 3 Real Numbers Compare, 5, and 4 using