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 continuedProperties 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

2 + 3 = 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 + 0 = 0 + 3 = 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 -4 + 4 = 0

9.Multiplicative Inverse Property

The multiplicative inverse property states that reciprocals multiply to 1.

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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.

6 + 8 = 8 + 6

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

12 + 0 = 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.

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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.

18 + -18 = 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 c2 – d2 for c= -3 and d= 5

Your Turn!

Try Ex. 6 Evaluate c (3-d) – c2 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 +10x2 , 5 and 10 are the coefficients

• Like terms have the same variables with the same exponents– Ex. 3t2 and -4t2

Ex.1 Simplify 4m2 + 3m – 2m2

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) -8 12- 4x

x2 + x + x2 - 0.5x

.5x – x 6x-5

5 – (4x-7) 2x2+ x

1-2 Homework

• Page 4 wb #1-11, #15-25