Alg 1 Adv: The Real Number System and Properties Study Guide

"What category includes all numbers on the number line?"

Real Numbers (R)

"What type of numbers are decimals that never end and have no pattern?"

Irrational Numbers (I)

"What set includes all fractions and decimals that end or repeat?"

Rational Numbers (Q)

"What set includes positive and negative whole numbers including zero?"

Integers (Z)

"What set includes non-negative numbers starting from zero (0, 1, 2, 3…)?"

Whole Numbers (W)

"What set includes counting numbers starting from one (1, 2, 3…)?"

Natural Numbers (N)

Which property states that order does not matter in addition or multiplication?

Commutative Property

Which property is shown by the example: 3 + 2 = 2 + 3?

Commutative Property of Addition

Which property states that the grouping of values does not matter?

Associative Property

"Which property is shown by the example: (a + b) + c = a + (b + c)?"

Associative Property

Which property states that a number keeps its identity when adding 0 or multiplying by 1?

Identity Property

Which property is shown by the example: a * 1 = a?

Identity Property of Multiplication

Which property uses opposites or reciprocals to cancel a value out?

Inverse Property

"Which property is shown by the example: 8 + (-8) = 0?"

Inverse Property of Addition

Which property is shown by the example: 2/3 * 3/2 = 1?

Inverse Property of Multiplication

Which property states that multiplying any number by 0 equals 0?

Zero Product Property

Which property is shown by the example: 30 * 0 = 0?

Zero Product Property

Which property allows you to multiply a value into terms inside parentheses?

Distributive Property

Which property is shown by the example: 2(x + 3) = 2x + 6?

Distributive Property

"Which property states that a value will always equal itself (e.g. 7 = 7)?"

Reflexive Property

"Which property allows you to flip an equation across the equals sign (if a = b then b = a)?"

Symmetric Property

"Which property is shown when 5x = 30 becomes 30 = 5x?"

Symmetric Property

"Which property states that if a = b and b = c

then a = c?",Transitive Property

"Which property is shown if 4 + 3 = 7 and 7 = √49 so 4 + 3 = √49?"

Transitive Property

What property states that an operation on a set always produces an element within that same set?

Closure Property

"True or False: Natural numbers are closed under subtraction."

False (Example: 2 - 3 = -1)

True or False: Even numbers are closed under addition.

True

"True or False: Irrational numbers are closed under division."

False (Example: π / π = 1)