Properties of Arithmetic

Properties of Arithmetic:

The properties of arithmetic define when the order of operations can be changed in an initial calculation, so that we can get a second calculation which is equal to the first obtained result. The arithmetic operations that involving real numbers and/or real extents that uses the properties of arithmetic.

There are three types of arithmetic properties. They are,

• Associative property
• Commutative property
• Distributive property

The addition or multiplication of a group of values is similar to the how the numbers are grouped. There are three or more values involved in associative property. The parenthesis refers the terms that are considered one unit. The combination (Associative Property) are within the parenthesis. Therefore, the values are 'associated' together. For multiplication, the product is always same as the grouping. In Associative Property grouping the brackets are done first.

Associative property of addition:

a+(b+c)=(a+b)+c

Associative property for multiplication:

a×(b×c)=(a×b)×c

Example:

Find the associative property of 2+(3+9) and 2(85)

Solution:

2+(3+9)=(2+3)+9

2×(8×5)=(2×8)×5)

Commutative property is the property that altering the order of the values and does not alter the final result. It is a basic property of many binary operations. Many mathematical proofs based on it.

Distributive property of addition:

a+b=b+a

Distributive property for multiplication:

ab=ba

Example:

Find the Commutative property for 4+6 and 6×9

Solution:

4+6=6+4

6×9=9×6

Distributive properties used to distributing something or we can split something or broken up into parts.

This is defined as,

a(b+c)=ab+ac

Example:

Multiply 3 x 17 by using the distributive law.

Solution:

Given 3 x 17
=3(10 +7)
=3(10) + 3(7)
=30 + 21
Therefore 3 x 17=51.