1. Section 1.1 Arron Morgan

2. Section 1.1: Real Numbers and Number Operations  Ordering Real Numbers (Number line)

3. Ordering numbers  -1/2, 2, 13/4, -3, -6 -6, -3, -1/2, 13/4, 2  1/6, 2.7, -1.5, -8, - 7 - 7 = -2.6 -8, -2.6, -1.5, 1/6, 2.7

4. Identifying Properties  Commutative  a+b=b+a or ab=ba  Associative  (a+b)+c=a+(b+c) or (ab)c=a(bc)  Identity  a+0=a,0+a=a or a*1=a,1*a=a  Inverse  a+(-a)=0 or a*1/a=1,a=0

5. Distributive Property  This property involves both addition and multiplication.  a(b+c)=ab+ac

6. Ex: Commutative  5+2=2+5  7=7  5*2=2*5  10=10  Commutative property states that numbers can be added or multiplied in any order. Commutative Property of Addition states that changing the order of addends does not change the sum. That is, a + b = b + a. Commutative Property of Multiplication states that changing the order of factors does not change the product. That is, a × b = b × a

7. Ex: Associative  (3+9)+8=3+(9+8)  12+8=3+17  20=20 - With this property, grouping does not matter

8. Ex: Identity  12(1)=12  12=12  Anything times one equals itself.

9. Ex: Distributive  2(5+11)=2*5+2*11  10+22=2*5+2*11  32=10+22  32=32  Distribute the 2 through the ()’s then solve.

10. Operations With real Numbers

11. The difference of 7 and -10 is:  7-(-10)=7+10  =17  Add 10, the opposite of -10  Simplify

12. The quotient of -24 and 1/3 is:  -24= -24*3 1/3  = - 72  Multiply by 3, the reciprocal of 1/3  Simplify "Men are liars. We'll lie about lying if we have to. I'm an algebra liar. I figure two good lies make a positive.". -- Tim Allen