# 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
• 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
• 2zebras - 0zebras = 2zebras
• 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

## 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
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

## 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
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.

## 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 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)