Chapter 1 Flashcards
Whole numbers
Any positive whole number, including zero
Integers
Any whole number, positive or negative, including zero
Rational numbers
Any number that terminates or repeats, includes fractions and everything.
Irrational numbers
Any endless non repeating number, like pi
Closure property of addition
A+ B = a real number
Closure property of multiplication
AB = a real number
Commutative property of addition
A+B=B+A
Commutative property of multiplication
Ab=bA
Associative property of addition
(A+b)+c= a+(b+c)
Associative property of multiplication
A(bc)=(ab)c
Identative property of addition
A+0=a a+0=a a is the additive identity
Identative property of multiplication
Ax1=a ax1=A a is the multiplicative identity
Inverse property of addition
A+(-a) = 0
Inverse property of multiplication
A x 1/A =1 A is not equal to 0
Distributive property
A(b+c) = ab+ac
When is an equation considered never true?
When you simplify it and get an untrue equation ex. 4=3
When is an equations considered sometimes true
When you simplify it and get a number x and another number ex. 4x=8
When is an equation considered always true
When you simplify it and are left with a true statement ex 6=6
The graph of an “and” equality….
Face each other making a section of answers that make both statements true
The graph of an “or” equation…
Will have arrows facing apart from eachother,
Steps for solving an absolute value equation
- Isolate the absolute value
- Set the 2 solutions (one negative, and one positive)
- Solve both
- Check for extraneous solutions
5 stop writing
Solving absolute value inequalities. |a|<b></b>
- Isolate the absolute value
2. Set up as -b<a></a>
Solving absolute value equations |a|>b “or”
- Isolate the absolute value
- Write as ab (flip sign for negative)
- Solve on both sides
- Check for extraneous solutions
- Stop writing.
Natural numbers
Any whole number that is positive, does not include zero
