Property Math Definition

Introduction for property math definition:

Mathematics plays an important role in our everyday life.  There are some different properties present in mathematics such as associative property, commutative property, distributive property and identity property.  In this content “property math definition”, we are going to discuss these types of properties.  Let us discuss some formulas and problems for these properties. Having problem with Differential Equations Solver keep reading my upcoming posts, i will try to help you.

Formula for Law – Property Math Definition

Associative property:

U + (V + W) = (U + V) + W

U `xx` (V `xx` W) = (U `xx` V) `xx` W

The answer will become same at both sides

For example,

If u = 2, v = 3 and w = 4

2 + (3 + 4) = (2 + 3) + 4

2 + 7 = 5 + 4

9 = 9

Commutative property:

Swap the numbers.

The answer will become same at both sides

For example:

U + V = V + U

U `xx` V = V `xx` U

For example,

If u = 2 and v = 3

2 + 3 = 3 + 2

5 = 5

Distributive property:

Add some numbers then multiply with added result

Multiply each parenthesis then add the values

(U + V) `xx` W = (U `xx` W) + (V `xx` W)

The answer will become same at both sides

For example,

If the value of u = 2, v = 3 and w = 4

(2 + 3) `xx` 4 = (2 `xx` 4) + (3 `xx` 4)

5 `xx` 4 = 8 + 12

20 = 20

Identity property:

If any number multiplied with the value one, the answer will become the same number

`1 xx U = U`

`U xx 1 = U`

For example,

The value of u is 2

`2 xx 1 = 2`

`1 xx 2 = 2`

Example Problems – Property Math Definition

Example problem 1 – Property math definition

Prove the commutative property for the value of u is 5 and v is 6.

Solution:

Given,

The value of u is 5

The value of v is 6

Formula of commutative law is X + Y = Y + X and X `xx` Y = Y `xx` X

X + Y = Y + X

5 + 6 = 6 + 5

11 = 11

X `xx` Y = Y `xx` X

5 `xx` 6 = 6 `xx` 5

30 = 30

Hence we proved the commutative property

Example problem 2 – Property math definition

Prove the associative property for the value of u is 3, v is 6 and w is 9.

Solution:

The value of u is 3

The value of v is 6

The value of w is 9

Formula for associative property is u + (v + w) = (u + v) + w and u `xx` (v `xx` w) = (u `xx` v) `xx` w

u + (v + w) = (u + v) + w

3 + (6 + 9) = (3 + 6) + 9

3 + 15 = 9 + 9

18 = 18

u `xx` (v `xx` w) = (u `xx` v) `xx` w

3 `xx` (6 `xx` 9) = (3 `xx` 6) `xx` 9

3 `xx` 54 = 18 `xx` 9

162 = 162

Hence we proved the associative property. Please express your views of this topic help in math homework by commenting on blog.

Practicing Problems – Property Math Definition

Practicing problem 1 – Property math definition

Prove the distributive property for the value of p is 11, q is 12 and r is 10.

Answer:  230

Practicing problem 2 – Property math definition

Prove the commutative property for the value of m is 20 and n is 15.

Answer:

m + n = n + m = 35

m `xx` n = n `xx` m = 300