Question

Hey please help, thank you!!

Answer 1

D

Explanation:

So we have the equation:

`A=(1)/(2)(12)(3+7)`

And we want to find out which of the answer choices is not equivalent.

Thus, let's go through each of the choices.

A)

We have:

`(12(3+7))/(2)`

This is correct.

Our original equation can be written as:

`A=(1)/(2)((12(3+7))/(1))`

And if we multiply straight across:

`A=(12(3+7))/(2)`

We'll get choice A. So choice A is correct.

B)

We have:

`6(3+7)`

This is also correct.

From our original equation:

`A=(1)/(2)(12)\cdot(3+7)`

If we multiply the first term together:

`A=6(3+7)`

We'll get choice B. So, choice B is correct.

C)

We have:

`0.5(12)(10)`

This is correct as well.

If we reduce 1/2 to decimal form and add the operations within the parentheses in the original equation, we will get:

`A=(1)/(2)(12)(3+7)\\A=0.5(12)(10)`

So, C is also correct.

D)

We have:

`(12)/(2)*(10)/(2)`

Note that this is not correct.

This attempted to use the distributive property. However, the distribute property does not work for multiplication. For instance:

`3(2+1)\text{ indeed equals } 3(2)+3(1)`

However:

`3(2*1)\text{ does not equal} 3(2)*3(1)`

So, choice D is not equivalent.

So choice D is our answer :)

If we evaluate it, we will get 30, in contrast to the 60 of the others.