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The associative and commutative are properties of operations defined on mathematical structures.

Both properties are concerned with the order - of operators or operands.

According to the ASSOCIATIVE property, the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c.

According to the COMMUTATIVE property the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a

For real numbers, both addition and multiplication are associative and commutative while subtraction and division are not. There are many mathematical structures in which a binary operation is not commutative - for example matrix multiplication.

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Q: How are the associative and commutative properties alike and different?

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They are alike in so far as they are properties of binary operations on elements of sets. T The associative property states that order in which operations are evaluated does not affect the result, while the commutative property states that the order of the operands does not make a difference. Basic binary operators are addition, subtraction, multiplication, division, exponentiation, taking logarithms. Basic operands are numbers, vectors, matrices.

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different they are made from different things

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They are both electromagnetic energy, just different frequencies, thus possessing very different properties and characteristics.

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Physical properties are those that can be observed without changing the identity of the substance. The general properties of matter such as color, density, hardness, are examples of physical properties. Properties that describe how a substance changes into a completely different substance are called chemical properties. Flammability and corrosion/oxidation resistance are examples of chemical properties.

they have similar properties

They are both alike and different.

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