# What are the Six Basic Laws of Mathematics Algebra

An online basic mathematics Algebra Laws printable

### Six Laws of Math Algebra

The Basic Laws of Algebra are the commutative law for addition, commutative law for multiplication, associative for addition, associative for multiplication, distributive law and zero laws.

## 1. Commutative Law For Addition

The arrangement of addends does not affect the sum.

Example:

x + y + z = z + x + y = y + x + z , where x = 5, y = 1, and z = 7

5 + 1 + 7 = 13

7 + 5 + 1 = 13

1 + 5 + 7 = 13

## 2. Commutative Law For Multiplication

The arrangement of factors does not affect the product.

Example:

x * y * z = z * x * y = y * x * z , where x = 4, y = 3, and z = 6

4 * 3 * 6 = 12 * 6 = 72

6 * 4 * 3 = 24 * 3 = 72

3 * 4 * 6 = 12 * 6 = 72

## 3. Associative Law For Addition

The grouping of addends does not affect the sum.

Example:

x + (y + z) = (x + y) + z , where x = 5, y = 1, and z = 7

5 + (1 + 7) = 5 + 8 = 13

(5 + 1) + 7 = 6 + 7 = 13

please note that regardless of how the numbers are grouped, the answer is still 13.

## 4. Associative Law For Multiplication

The grouping of factors does not affect the product.

Example:

(x * y) * z = x * (y * z) , where x = 4, y = 3, and z = 6

(4 * 3) * 6 = 12 * 6 = 72

4 * (3 * 6) = 4 * 18 = 72

The Associative Law works when we add or multiply. It does NOT work when we subtract or divide.

## 5. Distributive Law

Adding numbers and then multiplying them yields the same result as multiplying numbers and then adding them.

Example:

4 * (2 + 5 + 6) = 4 * 13 = 52 ……………. (i)

(4 *2) + (4*5) + (4*6) = 8 + 20 + 24 = 52 ……………. (ii)

The two equations (i) and (ii) are equal and both equal 52.

The distributive law involves a number or variable outside of parentheses ( a factor ) and numbers or variables inside parentheses separated by addition and/or subtraction signs ( terms ).

Multiply every term inside the parentheses by the factor outside it.

Example, distributive 5(2 + 6) will produce the same result as 5(2) + 5(6).

## 6. Zero Properties Law

The Zero Properties Law of multiplication says that any number multiplied by 0 equals 0.

Example:

155 * 0 = 0

0 * 3 = 0

The Zero Properties Law of addition says that any number plus 0 equals the same number.

155 + 0 = 155

0 + 3 = 3