Question

The product of three numbers does not change even if we change the ........................... of the numbers.

Answer 1

Answer:

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Step-by-step explanation:

The product of three or more numbers does not change if we change the grouping of the numbers. The product of a number and 1 is the number itself. The product of any number and zero is zero.

Answer 2

The product of three numbers does not change even if we change the order of the numbers.

• To solve this problem, we need to know the properties of the multiplication of numbers.

1. Commutative property: Multiplication of numbers is commutative, i.e. the order in which the numbers are multiplied does not matter. If a, and b are three numbers, then:  axb = bxa.
2. Associative property: When we multiply three numbers, the grouping of factors does not produce any change in the final answer, i.e if a,b, and c are three numbers, then: (axb)xc = ax(bxc).
3. Distributive property: This property states that multiplication can be distributed over addition and subtraction, i.e. if a,b, and c are three numbers, then: ax(b+c) = (axb)+(axc) and ax(b-c) = (axb)-(axc).
4. Identity property: It states that any number multiplied by 1 is the number itself.
5. Zero property: It states that any number multiplied by 0 is 0.

• From the above properties, specifically from the associative property of multiplication, we understand that the product of three numbers does not change even if we change the order of the numbers.
• Hence the correct answer is 'order'.