Quiz 1.1- Real Number System & Properties Flashcards
Real Numbers
R = All irrational and rational numbers
Irrational Numbers
I = All fractions and decimals that never end and have no repeating pattern (examples: Pi 3.1415…, square root of 24)
Rational Numbers
Q = All fractions and decimals that either repeat or terminate (examples: 5/6, -3.75, square root of 16, square root of 16/49, 2 and 1/5)
Integers
Z = All positive, negative, and neutral numbers with no decimals (examples: …,-2, -1, 0, 1, 2…, negative square root of 81, -24/8)
Whole Numbers
W = All positive and neutral numbers with no decimals (examples: 0, 1, 2, 3…, square root of 0)
Natural Numbers
N = All positive numbers with no decimals (examples: 1, 2, 3…, square root of 36)
Commutative Property
Order doesn’t matter with addition and multiplication (example: 5x + 2 = 2 + 5x)
Associative Property
Grouping doesn’t matter with addition and multiplication (example: (5 + 2) + 6 = 5 + (2 +6))
Identity Property
The value you start with is also the answer, “stays the same” (example: x + 0 = x, x * 1 = x)
Inverse Property
Use the opposite to “cancel”, think about multiplying by the reciprocal (example: 5x * 1/(5x) = 1)
Property of Zero
Anything multiplied by zero equals zero (example: x^2 * 0 = 0)
Distributive Property
Multiplying a value to everything inside parenthesis (example: 10(x + 5) = 10x + 50
Reflexive Property
A value is equal to itself, think about a reflection in a mirror (example: -15 = -15)
Symmetric Property
If a=b, then b=a (example: If x = -2, then -2 = x)
Transitive Property
If a=b and b=c, then a=c (example: If 4^2 = 16 and 16 = square root of 256, then 4^2 = square root of 256)
Which set of numbers is closed under subtraction? (Irrational numbers, Integers, Natural numbers, or Whole numbers)
Integers
Which of the following sets is NOT closed under addition? (Odd numbers, Whole numbers, Integers, or Natural numbers)
Odd numbers
