Question

What is equivalent to - 1/3 - (-4 + 1/6)

Answer 1

Step-by-step explanation:

In the given expression 1/6 is negative, because it's inside a parenthesis which has a negative sign before. In the same way, 4 is positive because it's negative inside the parenthesis but with the negative sign it becomes positive. And finally 1/3 is negative.

`-(1)/(3)+4-(1)/(6)`

Now we have to look at the options:

• A. ,It's not equivalent because there are no parenthesis and the signs don't match ( for example, 4 is negative and it has to be positive)

,

• B., It's not equivalent because 1/6 is positive and it has to be negative. Even if the other two numbers have the right sign.

,

• C., We have to eliminate the parenthesis first:

`-((1)/(3)-(1)/(6))+4=-(1)/(3)+(1)/(6)+4`

The sign of 1/6 is not right either.

• D., This is the same expression I wrote at the beginning of the explanation just in a different order, so this is equivalent

,

• E., We have to do the same as option C:

`-(1)/(3)-(4-(1)/(6))=-(1)/(3)-4+(1)/(6)`

The signs of 4 and 1/6 are wrong, so this is not equivalent.

• F., We do the same as before:

`4-((1)/(3)+(1)/(6))=4-(1)/(3)-(1)/(6)`

This expression is equivalent

Answer:

The equivalent expressions are options D and F