bellringer (copy at top of notes) #1.simplify | -9 – (-5) | #2. find the opposite and the...
TRANSCRIPT
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. 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.
515
1
23
32
1
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
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
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