60 lines
2.1 KiB
Markdown
60 lines
2.1 KiB
Markdown
---
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title: Basic Number Properties Associative, Commutative, and Distributive
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---
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## Basic Number Properties Associative, Commutative, and Distributive
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These are 3 basic properties of numbers.
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<br/>
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These properties play an important role in advanced mathematics. Textbooks generally don't discuss them in detail because all
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number systems we use upto high school follow these properties by default.
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<br/>
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When studying advanced mathematics we know the importance of these properties.
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# Properties one by one:
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## Associativity
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"To associate" means to form groups of operands.
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<br/>
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If an operation(e.g. +, -, ×, /) is associative it means, <strong>the result will remain same regardless of grouping of operands.</strong>
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<pre>
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for example, consider operation +,
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let, a = 3, b = 4, c = 5
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(a + b) + c = a + (b + c)
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->(3 + 4) + 5 = 3 + (4 + 5)
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-> 12=12
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</pre>
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###### try it with multiplication operation, & same variable values as above,
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### Note:
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+ All 4 basic arithmetic operations(i.e. +, -, ×, /) follow Associativity.
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<hr/><hr/><hr/>
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## Commutativity
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"To commute" means to move around, in this case, operands move around operator.
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<br/>
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If an operation(e.g. +, -, ×, /) is commutative it means, <strong>the result will remain same regardless of the order in which the operands are evaluated.</strong>
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<pre>
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for example, consider operation +,
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let, a = 3, b = 4
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a + b = b + a
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->3 + 4 = 4 + 3
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-> 7 = 7
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</pre>
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###### try it with multiplication operation, & same variable values as above,
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### Note:
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+ All 4 basic arithmetic operations(i.e. +, -, ×, /) follow Commutativity.
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<hr/><hr/><hr/>
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## Distributivity
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This property is easy to remember by knowing that "Multiplication is distributive over addition".
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Example,
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<br/>
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a × (b + c) = a × b + a × c
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i.e. Multiplication is performed separately on operands of addition and then addition is performed.
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<br/>
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<pre>
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3 × (4 + 5)
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-> 3 × 4 + 3 × 5
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-> 12 + 15
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-> 27
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</pre>
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### Note
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+ Multiplication is distributive over addtion, but vice versa is not true.
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