Answer:
D
Step-by-step explanation:
So we have the equation:
[tex]A=\frac{1}{2}(12)(3+7)[/tex]
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:
[tex]\frac{12(3+7)}{2}[/tex]
This is correct.
Our original equation can be written as:
[tex]A=\frac{1}{2}(\frac{12(3+7)}{1})[/tex]
And if we multiply straight across:
[tex]A=\frac{12(3+7)}{2}[/tex]
We'll get choice A. So choice A is correct.
B)
We have:
[tex]6(3+7)[/tex]
This is also correct.
From our original equation:
[tex]A=\frac{1}{2}(12)\cdot(3+7)[/tex]
If we multiply the first term together:
[tex]A=6(3+7)[/tex]
We'll get choice B. So, choice B is correct.
C)
We have:
[tex]0.5(12)(10)[/tex]
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:
[tex]A=\frac{1}{2}(12)(3+7)\\A=0.5(12)(10)[/tex]
So, C is also correct.
D)
We have:
[tex]\frac{12}{2}\times\frac{10}{2}[/tex]
Note that this is not correct.
This attempted to use the distributive property. However, the distribute property does not work for multiplication. For instance:
[tex]3(2+1)\text{ indeed equals } 3(2)+3(1)[/tex]
However:
[tex]3(2\times1)\text{ does not equal} 3(2)\times3(1)[/tex]
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.
