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title: Basic Number Properties Associative, Commutative, and Distributive
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## Basic Number Properties Associative, Commutative, and Distributive
These are 3 basic properties of numbers.
These properties play an important role in advanced mathematics. Textbooks generally don't discuss them in detail because all
number systems we use upto high school follow these properties by default.
When studying advanced mathematics we know the importance of these properties.
# Properties one by one:
## Associativity
"To associate" means to form groups of operands.
If an operation(e.g. +, -, ×, /) is associative it means, the result will remain same regardless of grouping of operands.
for example, consider operation +, let, a = 3, b = 4, c = 5 (a + b) + c = a + (b + c) ->(3 + 4) + 5 = 3 + (4 + 5) -> 12=12###### try it with multiplication operation, & same variable values as above, ### Note: + All 4 basic arithmetic operations(i.e. +, -, ×, /) follow Associativity.
for example, consider operation +, let, a = 3, b = 4 a + b = b + a ->3 + 4 = 4 + 3 -> 7 = 7###### try it with multiplication operation, & same variable values as above, ### Note: + All 4 basic arithmetic operations(i.e. +, -, ×, /) follow Commutativity.
3 × (4 + 5) -> 3 × 4 + 3 × 5 -> 12 + 15 -> 27### Note + Multiplication is distributive over addtion, but vice versa is not true.