Bellringer (copy at top of notes) #1.Simplify | -9 – (-5) | #2. Find the opposite and the reciprocal of 13/8. #3.Simplify 8 * 3 – 8 ÷ 4

1-1 continued Properties of Real Numbers

1. Commutative Property of Addition a + b = b + a When adding two numbers, the order of the numbers does not matter. Examples of the Commutative Property of Addition = 3 + 2(-5) + 4 = 4 + (-5)

2. Commutative Property of Multiplication a  b = b  a When multiplying two numbers, the order of the numbers does not matter. Examples of the Commutative Property of Multiplication 2  3 = 3  2(-3)  24 = 24  (-3)

3. Associative Property of Addition a + (b + c) = (a + b) + c When three numbers are added, it makes no difference which two numbers are added first. Examples of the Associative Property of Addition 2 + (3 + 5) = (2 + 3) + 5 (4 + 2) + 6 = 4 + (2 + 6)

4. Associative Property of Multiplication a(bc) = (ab)c When three numbers are multiplied, it makes no difference which two numbers are multiplied first. Examples of the Associative Property of Multiplication 2  (3  5) = (2  3)  5 (4  2)  6 = 4  (2  6)

5. Distributive Property a(b + c) = ab + ac Multiplication distributes over addition. Examples of the Distributive Property 2 (3 + 5) = (2  3) + (2  5) (4 + 2)  6 = (4  6) + (2  6)

6. Additive Identity Property The additive identity property states that if 0 is added to a number, the result is that number. Example: = = 3

7.Multiplicative Identity Property The multiplicative identity property states that if a number is multiplied by 1, the result is that number. Example: 5  1 = 1  5 = 5

8.Additive Inverse Property The additive inverse property states that opposites add to zero. 7 + (-7) = 0 and = 0

9.Multiplicative Inverse Property The multiplicative inverse property states that reciprocals multiply to 1.

Ex.1 Identify which property that justifies each of the following. 4  (8  2) = (4  8)  2

Ex.2 Identify which property that justifies each of the following = 8 + 6

Ex.3 Identify which property that justifies each of the following = 12

Ex.4 Identify which property that justifies each of the following. 5(2 + 9) = (5  2) + (5  9)

Ex.5 Identify which property that justifies each of the following. 5 + (2 + 8) = (5 + 2) + 8

Ex.6 Identify which property that justifies each of the following.

Ex.7 Identify which property that justifies each of the following. 5  24 = 24  5

Ex.8 Identify which property that justifies each of the following = 0

Ex.9 Identify which property that justifies each of the following. -34  1 = -34

1-2 “Algebraic expressions” To evaluate an algebraic expression you plug in numbers for the variables and follow the order of operations Recall PEMDAS: 1. Parentheses 2. Exponents 3. Multiply/Divide 4. Add/Subtract

1. Evaluating algebraic expressions Ex.1 Evaluate 7x-3xy for x= -2 and y= 5 Ex. 2 Evaluate x+y÷x for x=4 and y=2

Your Turn! Try Ex. 3: Evaluate 3x-4y+x-y for x=4 and y= -2

Ex. 4 Evaluate (k-18) 2 – 4k for k=6 Ex. 5 Evaluate c 2 – d 2 for c= -3 and d= 5

Your Turn! Try Ex. 6 Evaluate c (3-d) – c 2 for c= -3 and d=5

2. Combining like terms A term is a number, variable or a number and a variable written together A coefficient is the number in a term –Ex. For 5y +10x 2, 5 and 10 are the coefficients Like terms have the same variables with the same exponents –Ex. 3t 2 and -4t 2

Ex.1 Simplify 4m 2 + 3m – 2m 2 Ex.2 –(r - t) + 3(r + 2t)

Your turn! Try Ex. 3 2h – 3k + 7(2h-3k)

Last Ex. Find the perimeter of this figure

Index Cards Unsimplified (green)Simplified (yellow) 3(2x+1) x x 2 + x + x x.5x – x6x-5 5 – (4x-7)2x 2 + x

1-2 Homework Page 4 wb #1-11, #15-25