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)
