Did you realize that there are laws of math? If you do not follow them, you will not get a ticket, but they are handy to memorize and solve equations of all sorts quickly. The basic laws, or number properties, that apply to all math equations and operations are the identity property, commutative property, associative property and distributive property. Each is a distinct rule that always remains the same no matter what type of arithmetic operation you are using. Memorizing these properties can help you solve your mathematical problems quickly.

## What Is the Definition of the Identity Property of Addition?

The identity property of addition in math refers to the statement that the sum of zero and any other number is the number. No matter what you are adding to zero, the answer will always be the number it is added to.

For example, in a simple mathematical calculation, 1+0=1, 10+0=10 and so forth.

In algebraic calculations, a+0=a, z+0=z.

No matter what type of items you are adding, the rule will always apply in all math calculations.

## What Is the Identity Property in Math?

In addition to the additive identity property in math, there is a multiplication identity property. This rule states that the product of the number 1 and any other number is the number.

For example, in a simple mathematical calculation, 6*1=6, 8*1=8 and so forth.

In algebraic calculations the rule remains the same, for example, a*1=a and c*1=c.

This rule holds true for all multiplication problems in math calculations.

## What Is the Associative Property in Math?

The associative property in addition states that when you are adding, you can group the numbers together in any combination and get the same answer.

For example, 1+ (3+4) = (1+3) +4.

The Associative Property of multiplication states that when you multiply numbers you can also group them in any combination.

For example, 2*(3*5) = (2*3)*5.

## What Is the Commutative Property of Math?

The commutative property of addition states that you can add numbers in any order.

For example, 2+6=6+2=8.

The commutative property of multiplication states that you can multiply numbers in any order.

For example, 2*6=6*2=12

## What Is the Distributive Property of Math?

The distributive property of math is the same for addition and multiplication. It states that you can remove the brackets or parentheses in an expression, and then you multiply the value outside of the parenthesis by each of the terms in the parenthesis.

For example, in this equation, 6 (a + b), you can change it to 6 (a +b) =6a + 6b, and you will arrive at the same answer.