giao hoán

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The Vietnamese word "giao hoán" translates to "exchange" or "interchange" in English. It is often used in mathematical contexts, particularly in algebra, to describe operations where the order of elements does not affect the result.

Basic Explanation:

1. Meaning: "Giao hoán" refers to the process of swapping or exchanging one thing for another. In mathematics, it specifically indicates that changing the order of certain operations or numbers does not change the outcome.

Usage Instructions:

• You can use "giao hoán" in both everyday conversation and academic settings.
• In casual contexts, it might refer to exchanging items like books or gifts.
• In mathematics, it is commonly used when discussing properties of operations, such as addition and multiplication.

Examples:

1. Everyday Use:

   • "Chúng ta có thể giao hoán sách với nhau." (We can exchange books with each other.)

2. Mathematical Use:

   • "Phép cộng là phép giao hoán: a + b = b + a." (Addition is commutative: a + b = b + a.)

Advanced Usage:

In advanced mathematics, "giao hoán" can refer to the commutative property in algebra. This property states that the order of the numbers does not affect the sum or product.

Word Variants:

• "Giao hoán" can be used in various forms, such as:
  • "Tính giao hoán" (commutative calculation)
  • "Phép giao hoán" (commutative operation)

Different Meanings:

While "giao hoán" primarily means "exchange" or "interchange," in specific contexts, it can also imply a broader sense of interaction or interchangeability.

Synonyms:

• "Trao đổi" (exchange)
• "Đổi chác" (bartering)
• In mathematical contexts, it can be synonymous with "tính chất giao hoán" (commutative property).

Summary:

In summary, "giao hoán" is a versatile word used to describe both the act of exchanging items in everyday language and the concept of commutativity in mathematics.

Academic

1. Exchange, interchange
2. Commute
   • Đại số giao hoán
     Commulative algebra