commutative property of addition
changing the order of addends does not change the sum, i.e. if a and b are two real numbers, then a + b = b + a.
commutative property of multiplication
changing the order of factors does not change the product, i.e. if a and b are two real numbers, then a × b = b × a.
associative property of addition
when we add more than two numbers the grouping of the addends does not change the sum. (3 + 6) + 8 = 3 + (6 + 8)
associative property of multiplication
when we multiply more than two numbers the grouping of the factors does not change the product. (2 × 4) × 3 = 2 × (4 × 3)
identity property of addition
the sum of zero and any number or variable is the number or variable itself.
For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y
property of opposites
For every real number "a", there is a unique real number "-a" such that a + (-a) = 0 and (-a) + a = 0
the product of a number and a sum is equal to the sum of the individual products of the addends and the number.
That is, a(b + c) = ab + ac.
the same or equal
simplifying the expression
replacing an expression containing variables by an equivalent expression with as few terms as possible
identity property of multiplication
the product of 1 and any number or variable is the number or variable itself.
For example, 4 × 1 = 4, - 11 × 1 = - 11, y × 1 = y
numbers obtained by counting ones from any number in the set of integers
If the product of two numbers is 1, then the two numbers are said to be reciprocals of each other. The reciprocal of 'a' is .
property of reciprocals
For every nonzero real number "a", there is a unique real number "1/a" such that a x 1/a = 1 and 1/a x a = 1