Students are told that the order of numbers does not matter in addition, but it does matter for subtraction except when both numbers are identical, for example, 10-10 = 10-10 or 0.
When the two numbers are not the same, such as, 3 and 6, the pair of differences is opposites: one difference is a positive number (e.g., 4) and the other is its negative number (e.g., -4). This can be represented as a-b = c and b-a = -c. If a= b, then a-b = 0 and b- a = 0 = - 0. The pairs of differences sum to zero, such as, +4 + (-4) = 0.
Zero Property of Addition
The zero property of addition states that the sum of any number and 0 is that number: For example: 2 + 0 = 2, 99 + 0 = 99. The additive Inverse a + (-a) = 0, a-a = 0.
Zero Property of Multiplication
The zero property of multiplication states that the product of any number and 0 is 0. For Example: 2 x 0 = 0. This can be shown to be a consequence of the zero property of addition and the distributive rule.
Multiplicative Identity Property
The multiplicative identity property
states that the product of any number and one is that number, for example 5 x 1 = 5.