1. Properties of real numbers
Section 1.2
Properties of real numbers

2. 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

3. 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

4. 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

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

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

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

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

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

10. 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

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

12. 1-3 Square Roots

13. 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

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

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

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

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

18. Adding and Subtracting radicals
Must have like radicals

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