What Math Property Is

Introduction to properties in math:

Here we are going to see about the properties in math. There are many number of properties present in math. Among the many properties we often use associative, commutative and distributive property.  We are going to see about all the properties. The properties are,

Property 1: Reflexive property.
Property 2: Symmetric property.
Property 3: Transitive property.
Property 4: Commutative property.
Property 5: Associative property.
Property 6: Distributive property.
Property 7: Addition property.
Property 8: Multiplication property.
Property 9: Additive identity.
Property 10: Multiplicative identity.

Math properties


Properties in math:

Here we are going to see about the properties in detail.

Associative Property:

In this property, when we change the order for calculation it does not changes the answer.
The grouping of the numbers is not taken into consideration.
This property can be applied for the addtion operation and the multiplication operation.
The associative property is given as,
(x + y) + z = x + (y + z)

(x * y) * z = x * (y * z)

Commutative Property:

In this property the order for the addition or multiplication is reversed or interchanged it does not affect the resultant answer.
This property can be applied in addition operation and multiplication operation.
The commutative property is given as,
x + y = y + x

x * y = y * x

Distributive Property:

In this property it combines both the addition and multiplication.
The parenthesis is used to separate the operations of the addition and multiplication.
The distributive property is given as,
x (y +z) = x y + x z

Addition Property:

In this property we add the same non zero numbers to both sides.
Let us consider a as the non zero number then the addition property is given as,
x +a = y +a.

Multiplication Property:

This property is also same as the addition property instead to add the numbers here we are going to multiply the numbers.
The multiplication property is given as,
x * a = y *a.

Reflexive Property:

When the number is equal on both sides then it is referred as reflexive property.
The reflexive property in math is given as,
x =x.

Transitive Property:

When the two number are equal to the number in the third position then it is referred as transitive property in math.

Additive Identity:

When a zero is added to the number then we get the same number as the answer thus it is referred as the additive identity.
The additive identity property in math is given as,
x +0 = x.

Multiplication Identity:

When one is multiplied with a number we get the same number as the answer the multiplicative identity in math is given as,
x (1) = x.


Example Problems


Example problem for property in math:

Problem 1: Simplify: 4 (x+ 5) – 3x

Solution:

4(x + 5) – 3x = 4x +4*5 -3x --------- (according to the property of distributivity)

= 4x + 20 – 3x -------- (by simplifying 4*5 = 20)

= 4x – 3x + 20 -------- (according to the property of commutativity)

= x (4- 3) + 20 ------- (according to the property of distributivity)

= x (1) + 20 -------- (by simplifying 4-3 = 1)

= x +20.

Hence the answer is x +20.

Problem 2: Simplify: 2p + 5q – 6p

Solution:

2p + 5q – 6p  = 2p – 6p + 5q -------- (according to the property of commutativity)

= (2p – 6p) + 5q ------ (according to the property of associativity)

= p (2 – 6) + 5q -------- (according to the property of distributivity)

= p (-4) + 5q ---------- (simplifying 2 -6 = -4)

= -4p + 5q.

Hence the answer is -4p +5q.