Properties of real numbers Section 1.2 Properties of real numbers

5+(-5)=0 Additive identity Additive inverse For each real number, a, there is exactly one number, b, for which a+b=0 Ie 5+(-5)=0 Additive identity A number when added to x results in x What is this number? ZERO

Multiplicative inverse Multiplication (+)(+)= (+) (-)(+)= (-) (-)(-)= (+) Multiplicative inverse Aka Reciprocal For each non zero number a there is exactly one number b for which ab=1 To find the reciprocal of a number divide 1 by that number Ie 8 is reciprocal is 1/8

Is (-3/4) the reciprocal of (4/3) Question Is (-3/4) the reciprocal of (4/3) No because when multiplied together they do not = 1

Multiplicative identity A number that when multiplied by any number x give back x What is this number? 1

Addition Multiplication Commutative Property For any real a, b a + b = b + a Multiplication a b = b a

Addition Multiplication Associative Property For any real a, b, c a + (b + c) = (a + b) + c Multiplication a (b c) = (a b) c

Multiplicative Identity Property Write an expression equivalent to: x/(3y) by using 8/8 for 1

Additive identity property Write an expression equivalent to 4x – 2 by using 7y – 7y for 0

a ( b + c ) = ab + ac a ( b – c ) = ab – ac The Distributive Property For any real numbers a, b, c the following is true a ( b + c ) = ab + ac a ( b – c ) = ab – ac

Homework Pg17(1-3,7,8,21,52-55)

1-3 Square Roots

Square root The length of a side of a square is equal to the square root of its area. Principal square root, is the positive and negative value of the square root Ex principal √(4) = 2 or -2

Perfect squares Know the square root of the following 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169

Properties of square roots Square root of a product √(ab) = √(a) √(b) Square root of a quotient √(a/b) = √(a) /√(b)

Examples √(50) = √(25) √(2) = 5√(2) √(49/81) = √(49) /√(81) = 7/9

Rationalizing the Denominator YOU CAN NEVER HAVE A RADICAL IN THE DENOMINATOR!

Adding and Subtracting radicals Must have like radicals

Homework Pg24(6-10, 14,15,30,48,54)