Chapter 1 Flashcards
Equals Sign: =
2 expressions are fundamentally the same somehow.
Reflexive Property of Equality:
A=A
Symmetric Property of Equality:
A=B ↔️ B=A
Transitive Property of Equality:
A=B
@ 🔀 A=C
B=C
Set:
Collection of “objects”
- called elements of the set.
- members of the set.
Set notation:
Members separated by commas surrounded by 2 Braces.
-aka Roster method
{Red,Blue,Yellow} = {Yellow,Red,Blue}
Natural Numbers:
{1,2,3,4,5,6,…}
No zero
Whole Numbers:
{0,1,2,3,4,5,6,…}
Includes zero
Integers:
{...-4,-3,-2,-1,0,1,2,3,4...}
Includes
Zero
@
- numbers.Zero is
Neither Positive or Negative
≤:
Is less then or equal to
-8≤17
≥:
Is greater than or equal tp
25≥25
≠
Is not equal to
> :
Is greater than
-3>-10
How to think of - numbers:
Like the temperature.
Opposites -:
Same distance from 0 on the opposite side of 0 on the number line.
Ex. -(-9)=9, -(8)=-8
- if negative sign is in front means opposite of.
Absolute Value | |:
Of a number is the distance that number is from 0 on the number line regardless of direction.
-to calculate | | of a # just drop the - or +
Ex. |5|=5, |-5|=5
-|5|=-(5)=-5, -|-5|=-(5)=-5
Addition:
Means combine and count.
Addition: If # have the same sign:
- Add their | |
2. Use their common signs.
Addition: If # have opposite signs:
- Subtract their | |
2. Use the sign of the # with greater | |
Algebraic definition of Subtraction:
A-B = A+(-B)
When multiplying 2 same signed #:
- Multiply their | |
2. Answer is positive
When multiplying 2 opposite signed #:
- Multiply their | |
2. Answer is negative
Rational Numbers:
Are # that can be written as fraction of 2 integers where the Denominator is not 0.
Natural, Whole numbers and Integers all have in common?
They are all Rational #.
Rational # have:
Decimal forms that either
1. Terminate. 1/2 = 0.50
- Repeat. 1/3 = 0.3333
Irrational # have:
Decimal forms that do not terminate and do not repeat.
Ex. Pi≈3.14
Algebraic Definition of Division:
A÷B =A✖️1/B
Rational/Irrational taken together the gives:
Real Numbers
To add Fractions with the same #:
- ADD the numerators
- Keep the denominator the same
A/C+B/C=A+B/C
To Subtract fraction with the same denominator:
- Add the numerators
- Keep the denominator the same
- Remember subtract rule.
A/C-B/C=A/C+-B/C
The numerator:
Tells us how many pieces of that size.
Ex.
3/4= 3 pieces of 4
The denominator:
Tells us into how many equal-sized pieces the whole unit is split.
Ex. 1/4, 4 is equal to 1
Fundamental Principle of Fraction:
For all Real #
A,B and C can’t
B≠0, C≠0)
