1. Algebra II Chapter 2 2012

2. Parenthesis – anything grouped… including information above or below a fraction bar. Exponents – anything in the same family as a power… this includes radicals (square roots). Multiplication- this includes distributive property (discussed in detail later). Some items are grouped!!! Multiplication and Division are GROUPED from left to right (like reading a book- do whichever comes first. Addition and Subtraction are also grouped from left to right, do whichever comes first in the problem.

3. P Parenthesis E Exponents MD Multiplication and Division AS Addition and Subtraction In order from left to right

4. Parenthesis Exponents This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1 st ? Division did…now do the multiplication (indicated by parenthesis) More division Subtraction

5. Exponents Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication Parenthesis Division – because all the work is done above and below the line

6. P Parenthesis E Exponents M Multiplication D Division A Addition S Subtraction

7. Can you fill in the missing operations? 1. 2 - (3+5) + 4 = -2 2. 4 + 7 * 3 ÷ 3 = 11 3. 5 * 3 + 5 ÷ 2 = 10

8. Associative Properties Associative Properties Commutative Properties Commutative Properties Inverse Properties Inverse Properties Identity Properties Identity Properties Distributive Property Distributive Property All of these rules apply to Addition and Multiplication

9. Rules: Associative Property of Addition (a+b)+c = a+(b+c) Associative Property of Multiplication (ab)c = a(bc) It doesnt matter how you group (associate) addition or multiplication…the answer will be the same! Samples: Associative Property of Addition (1+2)+3 = 1+(2+3) Associative Property of Multiplication (2x3)4 = 2(3x4)

10. Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba It doesnt matter how you swap addition or multiplication around…the answer will be the same! Samples: Commutative Property of Addition 1+2 = 2+1 Commutative Property of Multiplication (2x3) = (3x2)

11. Does the Associative Property hold true for Subtraction and Division? Does the Commutative Property hold true for Subtraction and Division? Is 5-2 = 2-5? Is 6/3 the same as 3/6? Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Properties of real numbers are only for Addition and Multiplication

12. Rules: Inverse Property of Addition a+(-a) = 0 Inverse Property of Multiplication a(1/a) = 1 Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication 2(1/2)=1 What is the opposite (inverse) of addition? What is the opposite of multiplication? Subtraction (add the negative) Division (multiply by reciprocal)

13. Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2 What can you add to a number & get the same number back? What can you multiply a number by and get the number back? 0 (zero) 1 (one)

14. Rule: a(b+c) = ab+bc Samples: 4(3+2)=4(3)+4(2)=12+8=20 2(x+3) = 2x + 6 -(3+x) = -3 - x If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis.