Definition

1. Noun:
   • The result of multiplying two or more numbers or quantities together: A "mathematical product" is the number or expression that results from the operation of multiplication.

Usage

• The term "mathematical product" is used in arithmetic, algebra, and higher mathematics to specify the outcome of multiplication. It is a formal term often used to distinguish the result of multiplication from other types of "products" (e.g., commercial goods).
• It is typically used in explanatory or instructional contexts.

Examples

• Noun:
  • The mathematical product of 7 and 8 is 56.
  • In the equation 4 × 5 = 20, the number 20 is the mathematical product.
  • To find the area of the rectangle, calculate the mathematical product of its length and width.

Advanced Usage

• In algebraic expressions: The "mathematical product" can refer to the result of multiplying variables and constants.
  • In the expression (3x)(2y), the mathematical product is 6xy.
• In set theory or other mathematical operations: The term can sometimes be used more abstractly to denote the result of a multiplicative operation within a defined system (e.g., the product of two matrices).

Variants and Related Words

• Product (noun): The more common, shortened form. In a mathematical context, "product" is understood to mean "mathematical product."
  • The product of 10 and 10 is 100.
• Multiplicand (noun): A number that is to be multiplied by another.
• Multiplier (noun): A number by which another number (the multiplicand) is multiplied.
• Multiplication (noun): The arithmetic operation of combining groups of equal sizes.

Synonyms

• Result of multiplication: The outcome of a multiplication operation.
• Multiple (in specific contexts): Although "multiple" more commonly refers to a number that can be divided by another number without a remainder, it is related to the concept of repeated addition, which defines multiplication.

Related Phrases

• Dot product: Also called the scalar product, a specific type of mathematical product for vectors.
• Cross product: Also called the vector product, another specific operation in vector algebra.
• Cartesian product: In set theory, a set formed from all ordered pairs of elements from two given sets.

Related Idioms

Noun

1. a quantity obtained by multiplication
   • the product of 2 and 3 is 6