Identify the property illustrated in each statement. Assume all v...

Question

Identify the property illustrated in each statement. Assume all variables represent real numbers.

1 1
(5x) ( — ) = 5 ( x • — )
 x x

Accepted Answer

Hello, everyone. We are asked to write the name of the property used in the given statement, we are given 12 M multiplied by one divided by M equals 12, multiplied by the parentheses. M multiplied by one divided by M. Our answer choices are A, the community of property. B, the associative property C, the distributive property, the, the inverse property. So thinking about my options, if this was the inverse property, this would equal one or zero. So I know it's not the inverse property. If this were the distributive property, I would be multiplying things into parentheses. And that's not what I see here. So that gets us down to the community of property or the associative property. So thinking about the commutative property, this one is the one that says order doesn't matter. So that a multiplied by B would equal B multiplied by A. It's not exactly what we have going on here. Meanwhile, the associative property says that I could have a multiplied by the parentheses. B multiplied by C and that would be the same as having B multiplied by the parentheses. A multiplied by C. So let's see if that works. If we look at what we are given, we have 12 M. So those are kind of grouped together multiplied by one divided by M and that equals 12, multiplied by the parentheses M multiplied by one divided by M. So we changed the grouping, not necessarily the order. So our community of property talks about order where the associated property talks about grouping. Since I see the grouping changing and not the order. This is the associative property which is answer choice B have a nice day.

Identify the property illustrated in each statement. Assume all variables represent real numbers. 1 1 (5x) ( — ) = 5 ( x • — ) x x

Key Concepts

Properties of Equality

Distributive Property

Simplifying Fractions

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