SOLUTION: n which of the following does the original value decrease? I. The square of a fraction between -1 and 0 II. The square of a negative integer III. The cube of a negative integer

Question 896668: n which of the following does the original value decrease?
I. The square of a fraction between -1 and 0
II. The square of a negative integer
III. The cube of a negative integer less than -1
IV. the cube of a fraction between 0 and -1
a.)I only b.)II only c.)III only d.)I,II & III only e.) I,II,III & IV
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I.
the square of a negative number is always positive which will always be greater than the original negative number.

II.

the square of a negative integer will always be positive which will always be greater than the original negative number.

III.

the cube of a negative number will always be a larger negative number which will always be less than the original number.

example:

-2 cubed = -8 which is a larger negative number than -2 which makes it more negative which makes it less than -2.

so far selection III fits.

IV.

the cube of a fraction between 0 and -1.

the cube of a negative number between 0 and -1 will always be a smaller negative number which makes it less negative which makes it greater.

example:

-.9^3 = -.729 which is a smaller negative number which makes it less negative than -.9 which makes it greater than -.9

i believe selection III is the only one that fits the requirements.

more negative means less than.
less negative means greater than.
more positive means greater than.
less positive means less than.
all positive numbers are greater than any negative number.
all negative numbers are less than any positive number.
a larger negative means less than.
a smaller negative means greater than.
a larger positive means greater than.
a smaller positive means less than.

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