Properties of Numbers and Operations

 

Number sentence Addition and Subtracation Primary Conjecture   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

8 + 0 = 8
7 + 3 = 11
367 + 0 = 0
369 + 0 = 369
30 + 0 = 300
2 zebras + 0 zebras = 2 zebras
4z + 0 z = 4 z
x + 0 = 0
x + 0 = x

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

0 + 8 = 8
4 + 6 = 11
0 + 763 = 0
763 + 0 = 763
0 + 30 = 300
0 + 2 turtles = 2 turtles
0T + 3T = 3 T
0 + x = 0
X + 0 = 0

x + 0 = x

n - 0 = n When you subract zero from a number you get that same number.   8 - 0 = 8
7 - 3 = 10
367 - 0 = 0
369 - 0 = 369
30 - 0 = 3
2 zebras - 0 zebras = 2 zebras

4z - 0 z = 4 z
x - 0 = 0
x - 0 = x
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

3 - 3 = 0
3 - 2 = 0
8 - 8 = 0
2 trees - 2 trees = 0
2t - 2t = 0
b - b = 0
9 - b = 0
29 - n = 0
n - b = 0

       
Number sentence Multiplication and Division Primary   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

 
1 * n = n When you multiply 1 times a number, you get that number.    
n / 1 = n When you divide a number by 1, you get that number.    
n / n = 1, n ≠ 0 When you divide a number by itself you get one, except when the number is zero.    
n * n/1 = 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

 
Number sentence Multiplication and Division with zero   True/False Statements
n * 0 = 0
When you multiply a number times zero, you get zero.    
0 * n = 0 When you multiply a zero times a number, you get zero.    
0 / n = 0, a ≠ 0 When you divide zero by any number except zero you get zero.    
       
Number sentence Commutative properties for addition and multiplication   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 is the order in which a pair of addends is added does not affect the sum.

For all real numbers a and b, a + b = b + a

 
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 is the order in which a pair of factors is multiplied does not affect the product.

For all real numbers a and b, a * b = b * a

 
a * (b + c) =
(a * b) + (a * b)
 

Distributive property of multiplication over addition

For all real numbers a, b, c,
a * (b + c) = (a * b) + (a * b)