Question

Which expressions correctly demonstrate the Commutative Property?

3x⋅9y⋅6=9y⋅6⋅3x
3 x times 9 y times 6 equals 9 y times 6 times 3 x

3x⋅9y⋅6=9y+6+3x
3 x times 9 y times 6 equals 9 y plus 6 plus 3 x

3x(9y+6)=(3x+9y)⋅6
3 x left parenthesis 9 y plus 6 right parenthesis equals left parenthesis 3 x plus 9 y right parenthesis times 6

3x⋅9y⋅6=162xy

Answer 1

The Commutative Property refers to the ability to change the order of numbers in addition and multiplication without changing the result. This property applies to addition and multiplication but not to division or subtraction.

Let's analyze each expression to identify whether it correctly demonstrates the Commutative Property:

1. **3x⋅9y⋅6=9y⋅6⋅3x**
This expression correctly demonstrates the Commutative Property of multiplication. The order of the multiplicands has been changed, and the equality holds true.

2. **3x⋅9y⋅6=9y+6+3x**
This expression does not demonstrate the Commutative Property. It incorrectly states that a product equals a sum, which is not valid.

3. **3x(9y+6)=(3x+9y)⋅6**
This expression does not demonstrate the Commutative Property. It shows a distribution of multiplication over addition but does not involve changing the order of the factors.

4. **3x⋅9y⋅6=162xy**
This expression does not demonstrate the Commutative Property. It includes simplification (multiplying the values), which is not directly demonstrating the property of changing the order.

In summary, only the first expression **3x⋅9y⋅6=9y⋅6⋅3x** correctly demonstrates the Commutative Property.