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Questions and Answers
What is the definition of a 'product' in the context of multiplication?
In the expression 4 × 7 = 28, what is the product?
Which property of multiplication states that changing the order of factors does not alter the product?
If 2 and 5 are factors of a product, what is the product of these factors?
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What is unique about the product obtained from multiplying two numbers?
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In the expression 6 × 9 = 54, what are the factors?
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Which term refers to any number being multiplied in a multiplication problem?
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If you switch the order of multiplication in an expression from '3 × 6' to '6 × 3', will the product change?
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What is a primary characteristic of prime numbers when it comes to factors?
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'15' is obtained as the product of which two prime numbers?
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Study Notes
Multiplication Vocabulary: Product and Factor
Multiplication might be a simple arithmetic operation, but it comes with its own specialized vocabulary. Two key words for understanding multiplication are product and factor. Let's dive into these terms and discover their roles in the context of multiplication.
Product
The product of a multiplication operation is the result of the calculation. In other words, it's the answer to a multiplication problem. For example, when multiplying 3 by 5, the product is 15.
The product is often represented as the value following the multiplication sign (x or *). For example, in the expression 3 × 5 = 15, the product is 15.
Factor
Any of the numbers being multiplied in a multiplication problem is called a factor. In our previous example, 3 and 5 are both factors of the product 15.
Factors are crucial in understanding the properties of multiplication. For instance, the commutative property states that changing the order of factors does not alter the product. For example, both 3 × 5 = 15 and 5 × 3 = 15.
Factors also relate to prime numbers, which are only divisible by 1 and themselves. For instance, 3 and 5 are both prime numbers, and their product, 15, has no other prime factors besides 3 and 5.
Product as the Result of Multiplication
When we multiply two numbers, we obtain the product. It's important to note that the product is unique and depends on both factors. For example, 2 × 3 = 6 and 2 × 5 ≠6; the latter would be 10.
Factors as Building Blocks for Multiplication
Factors are the building blocks of multiplication problems. Every product can be represented as the result of multiplying its factors. For instance, 15 can be written as 3 × 5, and in this representation, 3 and 5 are the factors of the product 15.
In Summary
The product is the result of a multiplication problem, and the factors are the numbers being multiplied. Understanding these terms and their roles in the context of multiplication will help you to better understand the properties and operations of this fundamental arithmetic operation.
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Description
Learn about the key terms 'product' and 'factor' in the context of multiplication. Understand how factors contribute to the product in a multiplication operation and how the product is the result of multiplying two or more numbers.
