Properties Of Math

Introduction to math properties:

Mathematics is the important study which is applied in all fields. There are many properties in math. These properties define some of the rules and methods for solving the problems. Some of the properties in math are,

Associative property
Distributive property
Commutative property
Reflexive property
Transitive property
Addition property
Multiplication property
Additive identity
Symmetric property
Multiplication identity
Substitution property.



Math properties


Properties in math:

Here we are going to discuss about some of the properties in math.

Associative property:

In the associative property we does not consider the way that how the numbers are grouped with others. In this property when we rearrange the parenthesis it does not changes the value. This property is common for both addition and multiplication. The associative property is given as,

( p + q ) + r = p + ( q + r)

( p * q ) * r = p * ( q * r)

Commutative property:

In this commutative property we can swap the numbers after performing the operation. Since the value does not change even after the swapping or interchanging. This property is also common for both addition and multiplication. This commutative property is given as,

p + q = q + p

p * q = q * p

Distributive property:

In this distributive property, we can split and broken up the number of parts. The distributive property is given as,

p * (q +r) = p * q +p * r

Additive identity:

When we add zero to a number it results the same number as the answer. This property is referred as additive identity.

p + 0 = p.

Multiplicative identity:

When we multiply one to a number then it will result the same number as the answer which is referred as property of multiplicative identity. This property is given as,

( p ) 1 = p.

Addition property:

When two numbers such as p = q is given then if we add r to both numbers p and q then this property is referred as addition property. The addition property is given as,

p = q, p + r = q + r.

Multiplication property:

This property is same as the addition property but in this instead of addition we want to do multiplication. This multiplication property is given as,

p = q, pr = qr.


Example problems


Example problems by using the properties of math:

Problem 1: Simplify the given equation 4x – 5y + 8x.

Solution:

Given: 4x – 5y + 8x.

Step 1: By using the commutative property write the given equation as,

4x + 8x – 5y

Step 2: According to the associative property, write the equation as,

(4x + 8x) – 5y

Step 3: By using distributive property write the equation as,

x ( 4 + 8) – 5y

Step 4: Finally according to the commutative property and by doing the simplification, the equation is given as

12x – 5y

Problem 2: simplify: 7 ( x + 4).

Solution:

Given: 7(x + 4)

Step 1: By using the distributive property write the given equation as,

7x + 7 * 4 – 6x

Step 2: After doing simplification according to the commutative property, write the equation as,

7x – 6x +28

Step 3: By using associative property write the equation as,

( 7x – 6x ) + 28

Step 4: According to the distributive property, the equation is given as

x( 7 – 6) + 28

Step 5: According to the commutative property, the equation is given as,

x + 28.