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Properties of Real Numbers N: W: Z: Q: I: R: Natural (1,2,3, …) Whole (0,1,2,3,…) Integers (… -2,-1,0,1,2,…) Rationals (m/n; m,n integers) Irrational ( 2, , 7 , 3.45978) Real (all rational and irrational) Real Numbers, R I M A G I N A R Y Q I Z W N Properties of Real Numbers For any real numbers a, b, and c Addition Commutative a b ba Multiplication a *b b * a Associative (a b) c a (b c) (a * b)* c a *(b * c) Identity a+0=a=0+a a *1 a 1* a a (a ) 0 ( a) a If a is not zero, 1 then 1 Inverse a* a 1 a *a 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 ac=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 17 and 3.8 using < or > 17 4.123 17 3.8 or 3.8 17 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 17 , 5, and 4 using < or > 17 4.123 4 17 5