Properties
What are the order of operations?
The rules to be followed when simplifying expressions; Parenthesis, exponents, multiplication, division, addition, subtraction.
2+3(1+2)
11
2x+8+5x-15
7x-7
3x+12 when x=sqrt 64
36
If Joy has a square bedroom with an area of 81 square feet, what is one side length of her room?
9 feet
What is the identity property?
Addition: when 0 is added to any number, the answer is the number itself.
Multiplication: when 1 is multiplied by any number, the answer is the number itself
What property is being shown here?
Original: 3x+5(2x+1)=3x+10x+5
Distributive Property
-3n+2b-15b+8
-3n-13b+8
-5(x+3)+3x when x=3
-21
Decide whether each number is rational or irrational.
sqrt 56
8/7
0.98
Rational: 8/7, 0.98
Irrational: sqrt 56
What is the inverse property?
When a number is combined with its inverse, itis equal to the identity.
Multiplicative inverse: a*1/a=1
Additive Inverse: a+-a=0
(5a+3)+2a=(5a+2a)+3
Associative Property
12h+9+13h-20h
5h+9
0.5(6x+4) when x=12
38
How can I determine if a number is rational?
If it can be written as a ratio (fraction).
Fractions, integers, repeating or terminating decimals, perfect squares.
Answers will vary.
a(b+c)=ab+ac
Which two properties are being used here?
3(xy+2)+5xy
3xy+6+5xy
3xy+5xy+6
Distributive property and commutative property
3(x+1)+7x
10x+3
4x-3(x-1) when x=3
6
Half points: 10
Full points: 10 and -10
What is the difference between the associative and commutative properties?
Commutative is where the order doesn't matter.
Associative is where grouping doesn't affect the sum or product.
List what is happening at each step.
-5*(x+1)*2
-5*2*(x+1)
-10*(x+1)
-10x-10
Commutative property
Multiplication
Distribution
2(x-1)-4(x-3)
-2x+10
3(2x+3)-4(x+8) when x=6
-11
How do you earn points back from assignments, tests, and quizzes? Provide as much detail as you know.
Assignments: redo the problems and tell Ms Korpi
Quizzes and tests: complete a redo sheet and include a description of your new thoughts.