Properties of Numbers and Operations
Addition and Subtraction properties
Number sentence 
Primary Conjecture 
Property & conditions  True/False Statements 

n + 0 = n  When you add zero to a number you get that same number.  Identity property of addition: For every real number n + 0 = n 

0 + n = n  When you add a number to zero you get that same number. 


n  0 = n  When you subract zero from a number you get that same number.  Identity property of subtraction: For every real number n  0 = n 

n  n = n  When you subract a number from itself you get zero.  Inverse property of addition: For every real number n, there is a real number n such that n + (n) = 0 

Multiplication and Division properties
Number sentence 
Primary Conjecture 
Property & conditions  True/False Statements 

n * 1 = a  When you multiply a number times 1 you get that same number.  Identity property of multiplication: For all real numbers a, a * 1 = a 
3 * 1 = 3 
1 * n = n  When you multiply 1 times a number, you get that number.  1 * 4 = 4  
n / 1 = n  When you divide a number by 1, you get that number.  5 / 1 = 5  
n / n = 1, n ≠ 0  When you divide a number by itself you get one, except when the number is zero.  6 / 6 = 1  
n * 1/n = 1  Inverse property of multiplication: For every real number n, n ≠ 0, there is a real number 1/n such that n * 1/n = 1 
3 * 1/3 = 1 
Multiplication and Division with zero
Number sentence  Primary Conjecture  Property & conditions  True/False Statements 

n * 0 = 0 
When you multiply a number times zero, you get zero.  Property of zero  2 * 0 = 0 
0 * n = 0  When you multiply a zero times a number, you get zero.  0 * 3 = 0  
0 / n = 0, a ≠ 0 
When you divide zero by any number except zero you get zero.  0 / 0 = 0 
Commutative property for addition and multiplication
Number sentence  Primary Conjecture  Property & conditions  True/False Statements 

a + b = b + a  When you add two numbers, you can change the order of the numbers you add, and you wlll get the same answer.  Commutative property of addition: the order in which a pair of addends is added does not affect the sum. For all real numbers a and b, 
4 + 3 = 3 + 4 1 + (2 + 3) =

a * b = b * a  When you multiply two numbers, you can change the order of the numbers you multiply, and you will get the same answer.  Commutative property of multiplication: the order in which a pair of factors is multiplied does not affect the product. For all real numbers a and b, 
2 * 3 = 3 * 2 2 (3 * 4) = 2(4 * 3)

a * (b + c) = (a * b) + (a * b) 
Distributive property of multiplication over addition: For all real numbers a, b, c, 
2(3 * 4) = (2 * 3) + (2 * 4) 