Question

Identify the property in the following statements: $2\centerdot 8=8\centerdot 2?$

Answer 1

Hint: there are some basic properties present in the number system, these are commutative, distributive, associative and identity property.

Complete step by step answer:
Let’s understand one by one all the properties and see its application in the number system.
Commutative property: This property states that when you add two numbers or multiply two numbers then the arrangement of the numbers does not matter. For example: a+b=b+a and a*b=b*a (where a and b are any two numbers).
Distributive property: This property states that the sum of two numbers times a third number is equal to the sum of each number’s addend times the third number. Which is equal to a* (b + c) = (a * b) + (a * c) (where a, b, c is any three numbers).
Associative property: This property states that addition of any three numbers does not depend upon the arrangement of numbers. For example (a + b) + c= a + (b + c). and a * (b * c) = (a * b) * c.
Identity property: this property contains additive inverse property (i.e., what number is being added to a number as it remains the same after addition i.e., $0$) and multiplicative inverse property (what number is being multiplied to a number such that it remains the same number after multiplication i.e., $1$).
For example: a + $0$ = a and a*$1$ = a.
Therefore, the Answer is commutative property.

Note: There are four basic properties which you need to keep in mind as it helps in many topics of algebra, those properties are commutative, distributive, associative and identity.