Math Properties

Commutative (Order) Property of Addition:
Changing the order of the addends does not change the sum.

Example:

a+b = b+a

3+4 = 4+3

Commutative (Order) Property of Multiplication:
Changing the order of the factors does not change the product.

Example:

ab=ba

5x4 = 4x5


Inverse Property of Addition:
Adding the opposite (additive inverse) of a number to the number will give you a sum zero.

Example:

14 + (-14) = 0

(-14) + 14 = 0

a + (-a) = 0

(-a) + a = 0

Inverse Property of Multiplication:
If you multiply a number by its reciprocal (multiplicative inverse) the product is 1.

Example:

9 x 1/9 = 1

1/9 x 9 = 1

a x 1/a = 1

1/a x a = 1


Identity Property of Addition:
Adding zero to any number does not change the number.

Example:

a + 0 = a

0 + a = a

9 + 0 = 9

0 + 9 = 9

Identity Property of Multiplication:
Multiplying any number by 1 does not change the number.

Example:

a x 1 = a

1 x a = a

575 x 1 = 575

1 x 575 = 575

Zero Property of Multiplication:
The product of any number and 0 is 0.

Example:
a x 0 = 0

0 x a = 0

892 x 0 = 0

0 x 892 = 0


Associative (Grouping) Property of Addition:
Changing the grouping of three or more addends does not change the sum.

Example:

(a+b) + c = a + (b+c)

(6+2) + 7 = 6 + (2 +7)


Associative (Grouping) Property of Multiplication:
Changing the grouping of three or more factors does not change the product.

Example:

(a x b) x c = a x (b x c)

(8x3) x 7 = 8 x (7x3)

Distributive Property of Multiplication Over Addition:
Multiplying the sum of two numbers by a third number is the same as
multiplying each of the two numbers by that third number and adding the product.

Example:

a x (b+c) = (axb) + (axc)

3 x (6+4) = (3x6) + (3x4)

6 x (20 x 4) = (6 x 20) + (6 x 4)

The distributive property also applies to multiplication and subtraction.

4 x (7-5) = (4x7) – (4X5)


Mathematical Terms – Properties

Addends:
Two numbers you add together.

Sum:
Answer of two numbers added together.

Factor:
Two numbers you multiply.

Product:
Answer of two numbers multiplied together.

Dividend:
Number being separated into a certain number of equal groups.

Divisor:
Number you are dividing by in a division problem.

Quotient:
Answer to a division problem.