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Q: What is the property of addition and multiplication that makes it possible to change the order of the numbers and get the same answer?

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Addition and multiplication: yes

That is the commutative property of either multiplication or addition.

The distributive property OF MULTIPLICATION over addition is a*(b + c) = a*b + a*c for any numbers a, b and c.

No. The distributive property applies to two operations (usually multiplication and addition), NOT to numbers.

The distributive property is applicably to the operation of multiplication over either addition or subtraction of numbers. It does not apply to single numbers.

The distributive property of multiplication OVER addition (or subtraction) states that a*(b + c) = a*b + a*c Thus, multiplication can be "distributed" over the numbers that are inside the brackets.

Yes. The distributive property of multiplication over addition may help.

The answer cannot be addition of numbers because that sign can also go with the commutative property, not "only the associative property" as required by the question. For the same reason, the answer cannot be multiplication of numbers. Also, in both cases, multiplication is distributive over addition.

The commutative property of addition and the commutative property of multiplication.

That is non-commutativity. Matrix multiplication is non-commutative although addition still is.

The "distributive property" involves multiplication and addition, and there must be at least three numbers involved.

There is no such thing. The distributive property involves at least three numbers, and two operations (usually multiplication and addition).

For addition, 0 and for multiplication, 1.

The DISTRIBUTIVE (not distributed) property is a property of multiplication over addition (OR subtraction). In its simplest form, if x, y and z are three numbers then, according to the distributive property of multiplication over addition, x*(y + z) = x*y + x*z

The associative property. It works separately for addition and for multiplication.

That would be the associative property. The associative property applies to addition and multiplication, but not to subtraction or division.

Because of the distributive property of multiplication over addition.

Yes, it applies to even multiplication of fractions and rational and irrational numbers.

The associative power applies to an operation- such as multiplication or addition - not to specific numbers.

There is no property of multiplication that transposes numbers.

Yes. The commutative property of addition (as well as the commutative property of multiplication) applies to all real numbers, and even to complex numbers. As an example (for integers): 5 + (-3) = (-3) + 5

Mainly that in both cases, the numbers can be changed, in any order. This is related to the commucative property, as well as the associative property, which apply to both. - Also, in both cases there is a neutral element (0 for addition, 1 for multiplication).

Numbers do not have a distributive property. The distributive property is an attribute of one arithmetical operation over another. The main example is the distributive property of multiplication over addition.

a+(b+c)=(a+b)+c if you have multiple addition or multiplication numbers in parenthesis then the numbers in the parenthesis' order doesn't matter

The Abelian or commutative property of the multiplication of numbers. It is important that both "multiplication" and "numbers" feature in the answer. Because, it is applicable to multiplication but not, for example, for division. It is applicable for the multiplication on numbers but not matrices.