Properties
Number Properties
Commutative Property of Addition -
Addends can be added in any order and the sum will be the same.
Commutative Property of Multiplication -
Factors can be multiplied in any order and the product will be the same.
Associative Property of Addition -
Changing the grouping of addends will not change the sum. (the order of the addends does not change, just the grouping)
Associative Property of Multiplication -
Changing the grouping of factors will not change the product. (the order of the factors does not change, just the grouping)
Distributive Property -
You can multiply a number and a sum by multiplying each addend by the number and then adding the products together. The same applies to subtraction.
Inverse Property of Addition -
The sum of a number and its additive inverse (opposite) is zero.
Inverse Property of Multiplication -
The product of a nonzero number and its multiplicative inverse (reciprocal) is 1.
Identity Property of Addition -
The sum of a number and the additive identity (0) is the number.
Identity Property of Multiplication -
The product of a number and the multiplicative identity (1) is the number.
Cross Products Property -
The cross products of a proportion (numerator x denominator) are equal.
Example:
28 + 89 = 89 + 28
Algebra:
a + b = b + a
Example:
258 x 15 = 15 x 258
Algebra:
ab = ba
Example:
(5 + 8) + 7 = 5 +(8 +7)
Algebra:
(a +b) + c = a + (b + c)
Example:
(2.5 . 6) . 1.9 = 2.5 . (6 . 1.9)
Algebra:
(ab)c = a(bc)
Example:
12(9 + 7) = 12(9) + 12(7)
22(5 - 1) = 22(5) - 22(1)
Algebra:
a(b + c) = a(b) + a(c)
a(b - c) = a(b) - a(c)
Example:
2 + (-2) = 0
Algebra:
a + (-a) = 0
Example:
Algebra:
Example:
345 + 0 = 345
Algebra:
a + 0 = a
Example:
3.8 x 1 = 3.8
Algebra:
a .1 = a
Example:
3 x 8 = 4 x 6
Algebra:
